Automatic Matrix Calculation with Random Numbers
2018-12-15 09:05
This applet demonstrates automatic matrix calculations with elements generated as random numbers from 0 to 5. Using GeoGebra commands like Random and Mod, it dynamically creates random matrices and performs arithmetic. Integrating polygons, vectors, and lines, it visually illustrates the connection between matrix operations and geometric transformations, ideal for exploring linear algebra.
Loading the GeoGebra board and drawing, please wait…
<?xml version="1.0" encoding="utf-8"?>
<geogebra format="5.0" version="5.0.513.0" app="classic" platform="d" id="85588819-c94e-492e-9e93-e7235bdf3c47" xsi:noNamespaceSchemaLocation="http://www.geogebra.org/ggb.xsd" xmlns="" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" >
<gui>
<window width="1366" height="728" />
<perspectives>
<perspective id="tmp">
<panes>
<pane location="" divider="0.14641288433382138" orientation="1" />
</panes>
<views>
<view id="4097" visible="false" inframe="true" stylebar="true" location="1,1,1,1" size="400" window="165,2,1036,723" />
<view id="512" toolbar="0 | 1 501 5 19 , 67 | 2 15 45 18 , 7 37 | 514 3 9 , 13 44 , 47 | 16 | 551 550 11 , 20 22 21 23 , 55 56 57 , 12 | 69 | 510 511 , 512 513 | 533 531 , 534 532 , 522 523 , 537 536 , 535 | 521 520 | 36 , 38 49 560 | 571 30 29 570 31 33 | 17 | 540 40 41 42 , 27 28 35 , 6 , 502" visible="false" inframe="false" stylebar="false" location="1,1,1" size="500" window="100,100,600,400" />
<view id="4" toolbar="0 || 2020 , 2021 , 2022 , 66 || 2001 , 2003 , 2002 , 2004 , 2005 || 2040 , 2041 , 2042 , 2044 , 2043" visible="false" inframe="false" stylebar="false" location="1,1" size="300" window="100,100,600,400" />
<view id="8" toolbar="1001 | 1002 | 1003 || 1005 | 1004 || 1006 | 1007 | 1010 || 1008 1009 || 66 68 || 6" visible="false" inframe="false" stylebar="false" location="1,3" size="300" window="100,100,600,400" />
<view id="1" visible="true" inframe="false" stylebar="true" location="1" size="1339" window="100,100,600,400" />
<view id="2" visible="true" inframe="true" stylebar="true" location="3" size="200" window="25,37,1316,694" />
<view id="16" visible="false" inframe="false" stylebar="false" location="1" size="150" window="50,50,500,500" />
<view id="32" visible="false" inframe="false" stylebar="true" location="1" size="150" window="50,50,500,500" />
<view id="64" toolbar="0" visible="false" inframe="true" stylebar="true" location="1" size="150" window="50,50,500,500" />
<view id="70" toolbar="0 || 2020 || 2021 || 2022" visible="false" inframe="true" stylebar="true" location="1" size="150" window="50,50,500,500" />
</views>
<toolbar show="true" items="0 39 | 1 501 67 , 5 19 , 72 75 76 | 2 15 45 , 18 65 , 7 37 | 4 3 8 9 , 13 44 , 58 , 47 | 16 51 64 , 70 | 10 34 53 11 , 24 20 22 , 21 23 | 55 56 57 , 12 | 36 46 , 38 49 50 , 71 | 30 29 54 32 31 33 | 17 26 62 73 , 14 68 | 25 52 60 61 | 40 41 42 , 27 28 35 , 6" position="1" help="false" />
<input show="true" cmd="true" top="algebra" />
<dockBar show="true" east="true" />
</perspective>
</perspectives>
<labelingStyle val="2"/>
<font size="20"/>
</gui>
<euclidianView>
<viewNumber viewNo="1"/>
<size width="1339" height="523"/>
<coordSystem xZero="23.84943225787546" yZero="205.04527941382923" scale="66.65710285388296" yscale="66.65710285388316"/>
<evSettings axes="false" grid="false" gridIsBold="false" pointCapturing="3" rightAngleStyle="1" checkboxSize="26" gridType="0"/>
<bgColor r="255" g="250" b="205"/>
<axesColor r="102" g="204" b="255"/>
<gridColor r="129" g="168" b="211"/>
<lineStyle axes="1" grid="0"/>
<axis id="0" show="false" label="" unitLabel="" tickStyle="1" showNumbers="true"/>
<axis id="1" show="false" label="" unitLabel="" tickStyle="1" showNumbers="true"/>
</euclidianView>
<kernel>
<continuous val="false"/>
<usePathAndRegionParameters val="true"/>
<decimals val="2"/>
<angleUnit val="degree"/>
<algebraStyle val="0" spreadsheet="0"/>
<coordStyle val="0"/>
<startAnimation val="true"/>
</kernel>
<tableview min="-2.0" max="2.0" step="1.0"/>
<scripting blocked="false" disabled="false"/>
<construction title="Matrix Multiplication Animated Example" author="" date="">
<element type="point" label="A">
<show object="false" label="false" ev="4"/>
<objColor r="0" g="0" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<coords x="0.2798966960022347" y="2.2250322824993014" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<element type="point" label="B">
<show object="false" label="false" ev="4"/>
<objColor r="0" g="0" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<coords x="2.0" y="2.0" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<element type="point" label="C">
<show object="false" label="false" ev="4"/>
<objColor r="0" g="0" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<coords x="0.39991391333519544" y="1.1650236738328217" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<element type="point" label="D">
<show object="false" label="false" ev="4"/>
<objColor r="0" g="0" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<coords x="2.0" y="1.0" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<element type="point" label="E">
<show object="false" label="false" ev="4"/>
<objColor r="0" g="0" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<coords x="2.849978478333799" y="2.300043043332403" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<element type="point" label="F">
<show object="false" label="false" ev="4"/>
<objColor r="0" g="0" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<coords x="3.0" y="1.0" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<element type="point" label="G">
<show object="false" label="false" ev="4"/>
<objColor r="0" g="0" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<coords x="4.0" y="1.0" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<element type="point" label="H">
<show object="false" label="false" ev="4"/>
<objColor r="0" g="0" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<coords x="4.0" y="2.0" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<element type="point" label="I">
<show object="false" label="false" ev="4"/>
<objColor r="0" g="0" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<coords x="4.6699526523343575" y="2.3150451954990228" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<element type="point" label="J">
<show object="false" label="false" ev="4"/>
<objColor r="0" g="0" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<coords x="5.0" y="1.0" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<element type="point" label="K">
<show object="false" label="false" ev="4"/>
<objColor r="0" g="0" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<coords x="0.7433841576017808" y="2.274170420175636" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<expression label="text11" exp=""\left[ 
\begin{array}{c} 
\phantom{1} \\ \phantom{1} \\ \phantom{1} \\ \phantom{1}
\end{array}
\right.""/>
<element type="text" label="text11">
<show object="true" label="false" ev="20"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="1.0" size="0" style="1"/>
<startPoint exp="K"/>
<labelOffset x="-60" y="-3"/>
</element>
<expression label="text11_1" exp=""\left[ 
\begin{array}{c} 
\phantom{1} \\ \phantom{1} \\ \phantom{1} \\ \phantom{1}
\end{array}
\right.""/>
<element type="text" label="text11_1">
<show object="true" label="false" ev="20"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="1.0" size="0" style="1"/>
<startPoint x="2.324815701030913" y="2.3997254924630766" z="1.0"/>
</element>
<expression label="text11_2" exp=""\left] 
\begin{array}{c} 
\phantom{1} \\ \phantom{1} \\ \phantom{1} \\ \phantom{1}
\end{array}
\right.""/>
<element type="text" label="text11_2">
<show object="true" label="false" ev="20"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="1.0" size="0" style="1"/>
<startPoint x="1.9990357483206296" y="2.3880839697448737" z="1.0"/>
</element>
<expression label="text11_3" exp=""\left] 
\begin{array}{c} 
\phantom{1} \\ \phantom{1} \\ \phantom{1} \\ \phantom{1}
\end{array}
\right.\hspace{-0.35in}=""/>
<element type="text" label="text11_3">
<show object="true" label="false" ev="20"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="1.0" size="0" style="1"/>
<startPoint x="5.266036171367683" y="2.328075361078393" z="1.0"/>
</element>
<expression label="text11_4" exp=""\left] 
\begin{array}{c} 
\phantom{1} \\ \phantom{1} \\ \phantom{1} \\ \phantom{1}
\end{array}
\right.""/>
<element type="text" label="text11_4">
<show object="true" label="false" ev="20"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="1.0" size="0" style="1"/>
<startPoint x="17.32841200693735" y="2.358079665411634" z="1.0"/>
</element>
<expression label="text11_5" exp=""\left[ 
\begin{array}{c} 
\phantom{1} \\ \phantom{1} \\ \phantom{1} \\ \phantom{1}
\end{array}
\right.""/>
<element type="text" label="text11_5">
<show object="true" label="false" ev="20"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="1.0" size="0" style="1"/>
<startPoint x="6.073903979241733" y="2.253064600245292" z="1.0"/>
</element>
<element type="point" label="L">
<show object="false" label="false" ev="4"/>
<objColor r="0" g="0" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<coords x="0.6350602413108931" y="0.3604478990366241" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<expression label="f" exp="y = y(L)" type="line" />
<element type="line" label="f">
<show object="false" label="false" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<selectionAllowed val="false"/>
<coords x="0.0" y="1.0" z="-0.3604478990366241"/>
<lineStyle thickness="3" type="0" typeHidden="1"/>
<eqnStyle style="explicit"/>
</element>
<element type="point" label="M">
<show object="false" label="false" ev="4"/>
<objColor r="0" g="0" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<coords x="7.0" y="2.0" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<element type="point" label="N">
<show object="false" label="false" ev="4"/>
<objColor r="0" g="0" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<coords x="7.0" y="1.0" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<element type="point" label="O">
<show object="false" label="false" ev="4"/>
<objColor r="0" g="0" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<coords x="11.0" y="1.0" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<element type="point" label="P">
<show object="false" label="false" ev="4"/>
<objColor r="0" g="0" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<coords x="11.0" y="2.0" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<element type="point" label="Q">
<show object="false" label="false" ev="4"/>
<objColor r="0" g="0" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<coords x="15.0" y="2.0" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<element type="point" label="R">
<show object="false" label="false" ev="4"/>
<objColor r="0" g="0" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<coords x="15.0" y="1.0" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<expression label="text11_6" exp=""=\hspace{0.2in}\left[
\begin{array}{c} 
\phantom{1} \\ \phantom{1} \\ \phantom{1} \\ \phantom{1}
\end{array}
\right.""/>
<element type="text" label="text11_6">
<show object="true" label="false" ev="20"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="1.0" size="0" style="1"/>
<startPoint x="5.471761754635443" y="-1.6290240616331755" z="1.0"/>
</element>
<element type="point" label="S">
<show object="false" label="false" ev="4"/>
<objColor r="0" g="0" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<coords x="7.0" y="-1.0" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<element type="point" label="T">
<show object="false" label="false" ev="4"/>
<objColor r="0" g="0" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<coords x="6.534933282834777" y="-2.525075325831702" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<element type="point" label="U">
<show object="false" label="false" ev="4"/>
<objColor r="0" g="0" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<coords x="8.0" y="-2.0" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<element type="point" label="V">
<show object="false" label="false" ev="4"/>
<objColor r="0" g="0" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<coords x="8.0" y="-1.0" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<element type="point" label="W">
<show object="false" label="false" ev="4"/>
<objColor r="0" g="0" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<coords x="8.954993543500137" y="-1.630090390998042" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<element type="point" label="Z">
<show object="false" label="false" ev="4"/>
<objColor r="0" g="0" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<coords x="9.0" y="-2.0" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<expression label="text11_7" exp=""\left] 
\begin{array}{c} 
\phantom{1} \\ \phantom{1} \\ \phantom{1} \\ \phantom{1}
\end{array}
\right.""/>
<element type="text" label="text11_7">
<show object="true" label="false" ev="20"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="1.0" size="0" style="1"/>
<startPoint x="9.604582456281538" y="-1.6320758955150365" z="1.0"/>
</element>
<element type="numeric" label="t">
<value val="7.0"/>
<symbolic val="true" />
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
<layer val="0"/>
<labelMode val="1"/>
<slider min="1" max="38" absoluteScreenLocation="true" width="200.0" x="36.0" y="239.0" fixed="false" horizontal="true" showAlgebra="true"/>
<lineStyle thickness="10" type="0" typeHidden="1"/>
<animation step="1" speed="0.25" type="1" playing="true"/>
</element>
<command name="Mod">
<input a0="9" a1="6"/>
<output a0="a"/>
</command>
<element type="numeric" label="a">
<value val="3.0"/>
<symbolic val="true" />
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
<selectionAllowed val="false"/>
</element>
<element type="button" label="button1">
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelOffset x="564" y="191"/>
<labelMode val="0"/>
<fixed val="true"/>
<auxiliary val="true"/>
<ggbscript val="SetValue[t,If[t<38,t+1,0]]

"/>
<font serif="false" sizeM="2.0" size="20" style="0"/>
<caption val="Next"/>
</element>
<expression label="A_1" exp="A + (1.45, -0.46)" type="point" />
<element type="point" label="A_1">
<show object="false" label="false" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="1.7298966960022346" y="1.7650322824993014" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<command name="Polygon">
<input a0="A" a1="(x(A), y(A_1))" a2="A_1" a3="(x(A_1), y(A))"/>
<output a0="poly1" a1="a_1" a2="g" a3="a_2" a4="h"/>
</command>
<element type="polygon" label="poly1">
<lineStyle thickness="0" type="0" typeHidden="1"/>
<show object="true" label="false" ev="4"/>
<condition showObject="t ≤ 18 ∧ Mod[t, 6] ≠ 1 ∧ Mod[t, 6] ≠ 2"/>
<objColor r="255" g="0" b="0" alpha="0.11999999731779099"/>
<layer val="0"/>
<labelMode val="0"/>
</element>
<element type="segment" label="a_1">
<show object="true" label="false"/>
<objColor r="255" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<coords x="0.45999999999999996" y="0.0" z="-0.12875248016102792"/>
<lineStyle thickness="0" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="g">
<show object="true" label="false"/>
<objColor r="255" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<coords x="0.0" y="1.45" z="-2.559296809623987"/>
<lineStyle thickness="0" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="a_2">
<show object="true" label="false"/>
<objColor r="255" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<coords x="-0.45999999999999996" y="0.0" z="0.7957524801610276"/>
<lineStyle thickness="0" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="h">
<show object="true" label="false"/>
<objColor r="255" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<coords x="0.0" y="-1.45" z="3.226296809623987"/>
<lineStyle thickness="0" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<expression label="B_1" exp="E + (0.42, -1.5)" type="point" />
<element type="point" label="B_1">
<show object="false" label="false" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="3.269978478333799" y="0.8000430433324031" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<command name="Polygon">
<input a0="E" a1="(x(E), y(B_1))" a2="B_1" a3="(x(B_1), y(E))"/>
<output a0="poly2" a1="e" a2="i" a3="b_1" a4="j"/>
</command>
<element type="polygon" label="poly2">
<lineStyle thickness="0" type="0" typeHidden="1"/>
<show object="true" label="false" ev="4"/>
<condition showObject="Mod[t, 18] ≥ 3 ∧ Mod[t, 18] ≤ 6"/>
<objColor r="0" g="0" b="255" alpha="0.10000000149011612"/>
<layer val="0"/>
<labelMode val="0"/>
</element>
<element type="segment" label="e">
<show object="true" label="false"/>
<objColor r="0" g="0" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<coords x="1.5" y="0.0" z="-4.274967717500699"/>
<lineStyle thickness="0" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="i">
<show object="true" label="false"/>
<objColor r="0" g="0" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<coords x="0.0" y="0.41999999999999993" z="-0.33601807819960916"/>
<lineStyle thickness="0" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="b_1">
<show object="true" label="false"/>
<objColor r="0" g="0" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<coords x="-1.5" y="0.0" z="4.904967717500698"/>
<lineStyle thickness="0" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="j">
<show object="true" label="false"/>
<objColor r="0" g="0" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<coords x="0.0" y="-0.41999999999999993" z="0.9660180781996086"/>
<lineStyle thickness="0" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<expression label="C_1" exp="S + (2.58, -0.46)" type="point" />
<element type="point" label="C_1">
<show object="false" label="false" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="9.58" y="-1.46" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<expression label="D_1" exp="S + (0.58, -1.5)" type="point" />
<element type="point" label="D_1">
<show object="false" label="false" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="7.58" y="-2.5" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<expression label="E_1" exp="H + (0.42, -1.5)" type="point" />
<element type="point" label="E_1">
<show object="false" label="false" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="4.42" y="0.5" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<expression label="F_1" exp="V + (0.58, -1.5)" type="point" />
<element type="point" label="F_1">
<show object="false" label="false" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="8.58" y="-2.5" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<expression label="G_1" exp="I + (0.42, -1.5)" type="point" />
<element type="point" label="G_1">
<show object="false" label="false" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="5.0899526523343575" y="0.8150451954990228" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<command name="Polygon">
<input a0="I" a1="(x(I), y(G_1))" a2="G_1" a3="(x(G_1), y(I))"/>
<output a0="poly7" a1="i_1" a2="c" a3="g_1" a4="d"/>
</command>
<element type="polygon" label="poly7">
<lineStyle thickness="0" type="0" typeHidden="1"/>
<show object="true" label="false" ev="4"/>
<condition showObject="Mod[t, 18] ≥ 15 ∨ Mod[t, 18] ≟ 0"/>
<objColor r="0" g="0" b="255" alpha="0.10000000149011612"/>
<layer val="0"/>
<labelMode val="0"/>
</element>
<element type="segment" label="i_1">
<show object="true" label="false"/>
<objColor r="0" g="0" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<coords x="1.5" y="0.0" z="-7.004928978501535"/>
<lineStyle thickness="0" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="c">
<show object="true" label="false"/>
<objColor r="0" g="0" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<coords x="0.0" y="0.41999999999999993" z="-0.34231898210958933"/>
<lineStyle thickness="0" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="g_1">
<show object="true" label="false"/>
<objColor r="0" g="0" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<coords x="-1.5" y="0.0" z="7.634928978501536"/>
<lineStyle thickness="0" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="d">
<show object="true" label="false"/>
<objColor r="0" g="0" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<coords x="0.0" y="-0.41999999999999993" z="0.9723189821095897"/>
<lineStyle thickness="0" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<expression label="H_1" exp="W + (0.58, -1.5)" type="point" />
<element type="point" label="H_1">
<show object="false" label="false" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="9.534993543500137" y="-3.130090390998042" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<command name="Polygon">
<input a0="W" a1="(x(W), y(H_1))" a2="H_1" a3="(x(H_1), y(W))"/>
<output a0="poly8" a1="w" a2="j_1" a3="h_2" a4="k_1"/>
</command>
<element type="polygon" label="poly8">
<lineStyle thickness="0" type="0" typeHidden="1"/>
<show object="true" label="false" ev="4"/>
<condition showObject="Mod[t, 18] ≥ 15 ∨ Mod[t, 18] ≟ 0"/>
<objColor r="0" g="0" b="255" alpha="0.10000000149011612"/>
<layer val="0"/>
<labelMode val="0"/>
</element>
<element type="segment" label="w">
<show object="true" label="false"/>
<objColor r="0" g="0" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<coords x="1.5" y="0.0" z="-13.432490315250206"/>
<lineStyle thickness="0" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="j_1">
<show object="true" label="false"/>
<objColor r="0" g="0" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<coords x="0.0" y="0.5800000000000001" z="1.8154524267788652"/>
<lineStyle thickness="0" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="h_2">
<show object="true" label="false"/>
<objColor r="0" g="0" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<coords x="-1.5" y="0.0" z="14.302490315250207"/>
<lineStyle thickness="0" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="k_1">
<show object="true" label="false"/>
<objColor r="0" g="0" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<coords x="0.0" y="-0.5800000000000001" z="-0.9454524267788642"/>
<lineStyle thickness="0" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<expression label="I_1" exp="C + (1.45, -0.46)" type="point" />
<element type="point" label="I_1">
<show object="false" label="false" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="1.8499139133351954" y="0.7050236738328217" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<command name="Polygon">
<input a0="C" a1="(x(C), y(I_1))" a2="I_1" a3="(x(I_1), y(C))"/>
<output a0="poly9" a1="c_2" a2="l_1" a3="i_2" a4="m_1"/>
</command>
<element type="polygon" label="poly9">
<lineStyle thickness="0" type="0" typeHidden="1"/>
<show object="true" label="false" ev="4"/>
<condition showObject="t > 18 ∧ Mod[t, 6] ≠ 1 ∧ Mod[t, 6] ≠ 2"/>
<objColor r="255" g="0" b="0" alpha="0.10000000149011612"/>
<layer val="0"/>
<labelMode val="0"/>
</element>
<element type="segment" label="c_2">
<show object="true" label="false"/>
<objColor r="255" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<coords x="0.45999999999999996" y="0.0" z="-0.18396040013418985"/>
<lineStyle thickness="0" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="l_1">
<show object="true" label="false"/>
<objColor r="255" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<coords x="0.0" y="1.45" z="-1.0222843270575914"/>
<lineStyle thickness="0" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="i_2">
<show object="true" label="false"/>
<objColor r="255" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<coords x="-0.45999999999999996" y="0.0" z="0.8509604001341899"/>
<lineStyle thickness="0" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="m_1">
<show object="true" label="false"/>
<objColor r="255" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<coords x="0.0" y="-1.45" z="1.6892843270575915"/>
<lineStyle thickness="0" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Random">
<input a0="0" a1="5"/>
<output a0="a11"/>
</command>
<element type="numeric" label="a11">
<value val="4.0"/>
<symbolic val="true" />
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
<algebra labelVisible="false"/></element>
<command name="Random">
<input a0="0" a1="5"/>
<output a0="a12"/>
</command>
<element type="numeric" label="a12">
<value val="5.0"/>
<symbolic val="true" />
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
<algebra labelVisible="false"/></element>
<command name="Random">
<input a0="0" a1="5"/>
<output a0="b11"/>
</command>
<element type="numeric" label="b11">
<value val="0.0"/>
<symbolic val="true" />
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
<algebra labelVisible="false"/></element>
<command name="Random">
<input a0="0" a1="5"/>
<output a0="b12"/>
</command>
<element type="numeric" label="b12">
<value val="4.0"/>
<symbolic val="true" />
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
<algebra labelVisible="false"/></element>
<command name="Random">
<input a0="0" a1="5"/>
<output a0="m"/>
</command>
<element type="numeric" label="m">
<value val="4.0"/>
<objColor r="0" g="0" b="255" alpha="0.0"/>
<algebra labelVisible="false"/></element>
<command name="Random">
<input a0="0" a1="5"/>
<output a0="n"/>
</command>
<element type="numeric" label="n">
<value val="0.0"/>
<symbolic val="true" />
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
<algebra labelVisible="false"/></element>
<command name="Polygon">
<input a0="T" a1="(x(T), y(H_1))" a2="H_1" a3="(x(H_1), y(T))"/>
<output a0="poly10" a1="t_1" a2="n_1" a3="h_3" a4="p_1"/>
</command>
<element type="polygon" label="poly10">
<lineStyle thickness="0" type="0" typeHidden="1"/>
<show object="true" label="false" ev="4"/>
<condition showObject="t > 18 ∧ Mod[t, 6] ≠ 1 ∧ Mod[t, 6] ≠ 2"/>
<objColor r="255" g="0" b="0" alpha="0.10000000149011612"/>
<layer val="0"/>
<labelMode val="0"/>
</element>
<element type="segment" label="t_1">
<show object="true" label="false"/>
<objColor r="255" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<coords x="0.6050150651663402" y="0.0" z="-3.953733085971969"/>
<lineStyle thickness="0" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="n_1">
<show object="true" label="false"/>
<objColor r="255" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<coords x="0.0" y="3.000060260665361" z="9.390459794323728"/>
<lineStyle thickness="0" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="h_3">
<show object="true" label="false"/>
<objColor r="255" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<coords x="-0.6050150651663402" y="0.0" z="5.768814740081371"/>
<lineStyle thickness="0" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="p_1">
<show object="true" label="false"/>
<objColor r="255" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<coords x="0.0" y="-3.000060260665361" z="-7.575378140214326"/>
<lineStyle thickness="0" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Random">
<input a0="0" a1="5"/>
<output a0="p"/>
</command>
<element type="numeric" label="p">
<value val="1.0"/>
<objColor r="0" g="0" b="255" alpha="0.0"/>
<algebra labelVisible="false"/></element>
<command name="Random">
<input a0="0" a1="5"/>
<output a0="q"/>
</command>
<element type="numeric" label="q">
<value val="3.0"/>
<symbolic val="true" />
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
<algebra labelVisible="false"/></element>
<command name="Random">
<input a0="0" a1="5"/>
<output a0="v"/>
</command>
<element type="numeric" label="v">
<value val="3.0"/>
<objColor r="0" g="0" b="255" alpha="0.0"/>
<algebra labelVisible="false"/></element>
<command name="Random">
<input a0="0" a1="5"/>
<output a0="s"/>
</command>
<element type="numeric" label="s">
<value val="5.0"/>
<objColor r="255" g="0" b="255" alpha="0.0"/>
<algebra labelVisible="false"/></element>
<expression label="text1" exp=""" + a11 + """ />
<element type="text" label="text1">
<show object="true" label="false" ev="4"/>
<objColor r="255" g="0" b="0" alpha="0.0" dynamicr="If[t ≤ 18 ∧ Mod[t, 6] ≠ 1 ∧ Mod[t, 6] ≠ 2, 1, 0]" dynamicg="0" dynamicb="0" colorSpace="0"/>
<layer val="0"/>
<labelMode val="0"/>
<algebra labelVisible="false"/> <font serif="true" sizeM="2.0" size="20" style="1"/>
<startPoint exp="A"/>
<labelOffset x="3" y="27"/>
</element>
<expression label="text2" exp=""" + (LaTeX[a12]) + """ />
<element type="text" label="text2">
<show object="true" label="false" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0.0" dynamicr="If[t ≤ 18 ∧ Mod[t, 6] ≠ 1 ∧ Mod[t, 6] ≠ 2, 1, 0]" dynamicg="0" dynamicb="0" colorSpace="0"/>
<layer val="0"/>
<labelMode val="0"/>
<algebra labelVisible="false"/> <isLaTeX val="true"/>
<font serif="true" sizeM="2.0" size="20" style="1"/>
<startPoint exp="B"/>
<labelOffset x="-48" y="-30"/>
</element>
<expression label="text3" exp=""" + (LaTeX[b11]) + """ />
<element type="text" label="text3">
<show object="true" label="false" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0.0" dynamicr="If[t > 18 ∧ Mod[t, 6] ≠ 1 ∧ Mod[t, 6] ≠ 2, 1, 0]" dynamicg="0" dynamicb="0" colorSpace="0"/>
<layer val="0"/>
<labelMode val="0"/>
<algebra labelVisible="false"/> <isLaTeX val="true"/>
<font serif="true" sizeM="2.0" size="20" style="1"/>
<startPoint exp="C"/>
<labelOffset x="-8" y="-18"/>
</element>
<expression label="text4" exp=""" + (LaTeX[b12]) + """ />
<element type="text" label="text4">
<show object="true" label="false" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0.0" dynamicr="If[t > 18 ∧ Mod[t, 6] ≠ 1 ∧ Mod[t, 6] ≠ 2, 1, 0]" dynamicg="0" dynamicb="0" colorSpace="0"/>
<layer val="0"/>
<labelMode val="0"/>
<algebra labelVisible="false"/> <isLaTeX val="true"/>
<font serif="true" sizeM="2.0" size="20" style="1"/>
<startPoint exp="D"/>
<labelOffset x="-47" y="-28"/>
</element>
<expression label="text5" exp=""" + (LaTeX[m]) + """ />
<element type="text" label="text5">
<show object="true" label="false" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0.0" dynamicr="0" dynamicg="0" dynamicb="If[Mod[t, 18] ≥ 3 ∧ Mod[t, 18] ≤ 6, 1, 0]" colorSpace="0"/>
<layer val="0"/>
<labelMode val="0"/>
<algebra labelVisible="false"/> <isLaTeX val="true"/>
<font serif="true" sizeM="2.0" size="20" style="1"/>
<startPoint exp="E"/>
<labelOffset x="-8" y="-8"/>
</element>
<expression label="text6" exp=""" + (LaTeX[s]) + """ />
<element type="text" label="text6">
<show object="true" label="false" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0.0" dynamicr="0" dynamicg="0" dynamicb="If[Mod[t, 18] ≥ 9 ∧ Mod[t, 18] ≤ 12, 1, 0]" colorSpace="0"/>
<layer val="0"/>
<labelMode val="0"/>
<algebra labelVisible="false"/> <isLaTeX val="true"/>
<font serif="true" sizeM="2.0" size="20" style="1"/>
<startPoint exp="H"/>
<labelOffset x="-27" y="-29"/>
</element>
<expression label="text7" exp=""" + (LaTeX[p]) + """ />
<element type="text" label="text7">
<show object="true" label="false" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0.0" dynamicr="0" dynamicg="0" dynamicb="If[Mod[t, 18] ≥ 15 ∨ Mod[t, 18] ≟ 0, 1, 0]" colorSpace="0"/>
<layer val="0"/>
<labelMode val="0"/>
<algebra labelVisible="false"/> <isLaTeX val="true"/>
<font serif="true" sizeM="2.0" size="20" style="1"/>
<startPoint exp="I"/>
<labelOffset x="-4" y="-4"/>
</element>
<expression label="text8" exp=""" + (LaTeX[n]) + """ />
<element type="text" label="text8">
<show object="true" label="false" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0.0" dynamicr="0" dynamicg="0" dynamicb="If[Mod[t, 18] ≥ 3 ∧ Mod[t, 18] ≤ 6, 1, 0]" colorSpace="0"/>
<layer val="0"/>
<labelMode val="0"/>
<algebra labelVisible="false"/> <isLaTeX val="true"/>
<font serif="true" sizeM="2.0" size="20" style="1"/>
<startPoint exp="F"/>
<labelOffset x="-17" y="-36"/>
</element>
<expression label="text12" exp=""(" + (LaTeX[a11]) + ")(" + (LaTeX[m]) + ")+(" + (LaTeX[a12]) + ")(" + (LaTeX[n]) + ")"" />
<element type="text" label="text12">
<show object="true" label="false" ev="4"/>
<condition showObject="t ≥ 7"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<algebra labelVisible="false"/> <isLaTeX val="true"/>
<font serif="true" sizeM="1.0" size="0" style="1"/>
<startPoint exp="M"/>
<labelOffset x="-31" y="-21"/>
</element>
<expression label="text13" exp=""(" + (LaTeX[a11]) + ")(" + (LaTeX[s]) + ")+(" + (LaTeX[a12]) + ")(" + (LaTeX[v]) + ")"" />
<element type="text" label="text13">
<show object="true" label="false" ev="4"/>
<condition showObject="t ≥ 13"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<algebra labelVisible="false"/> <isLaTeX val="true"/>
<font serif="true" sizeM="1.0" size="0" style="1"/>
<startPoint exp="P"/>
<labelOffset x="-58" y="-17"/>
</element>
<expression label="text14" exp=""(" + (LaTeX[a11]) + ")(" + (LaTeX[p]) + ")+(" + (LaTeX[a12]) + ")(" + (LaTeX[q]) + ")"" />
<element type="text" label="text14">
<show object="true" label="false" ev="4"/>
<condition showObject="t ≥ 19"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<algebra labelVisible="false"/> <isLaTeX val="true"/>
<font serif="true" sizeM="1.0" size="0" style="1"/>
<startPoint exp="Q"/>
<labelOffset x="-78" y="-19"/>
</element>
<expression label="text15" exp=""(" + (LaTeX[b11]) + ")(" + (LaTeX[m]) + ")+(" + (LaTeX[b12]) + ")(" + (LaTeX[n]) + ")"" />
<element type="text" label="text15">
<show object="true" label="false" ev="4"/>
<condition showObject="t ≥ 25"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<algebra labelVisible="false"/> <isLaTeX val="true"/>
<font serif="true" sizeM="1.0" size="0" style="1"/>
<startPoint exp="N"/>
<labelOffset x="-30" y="-13"/>
</element>
<expression label="text16" exp=""(" + (LaTeX[b11]) + ")(" + (LaTeX[s]) + ")+(" + (LaTeX[b12]) + ")(" + (LaTeX[v]) + ")"" />
<element type="text" label="text16">
<show object="true" label="false" ev="4"/>
<condition showObject="t ≥ 31"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<algebra labelVisible="false"/> <isLaTeX val="true"/>
<font serif="true" sizeM="1.0" size="0" style="1"/>
<startPoint exp="O"/>
<labelOffset x="-54" y="-16"/>
</element>
<expression label="text17" exp=""(" + (LaTeX[b11]) + ")(" + (LaTeX[p]) + ")+(" + (LaTeX[b12]) + ")(" + (LaTeX[q]) + ")"" />
<element type="text" label="text17">
<show object="true" label="false" ev="4"/>
<condition showObject="t ≥ 37"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<algebra labelVisible="false"/> <isLaTeX val="true"/>
<font serif="true" sizeM="1.0" size="0" style="1"/>
<startPoint exp="R"/>
<labelOffset x="-77" y="-17"/>
</element>
<expression label="c11" exp="(a11 * m) + (a12 * n)" />
<element type="numeric" label="c11">
<value val="16.0"/>
<symbolic val="true" />
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
</element>
<expression label="c12" exp="(a11 * s) + (a12 * v)" />
<element type="numeric" label="c12">
<value val="35.0"/>
<symbolic val="true" />
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
</element>
<expression label="c21" exp="(b11 * m) + (b12 * n)" />
<element type="numeric" label="c21">
<value val="0.0"/>
<symbolic val="true" />
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
</element>
<expression label="c22" exp="(b11 * s) + (b12 * v)" />
<element type="numeric" label="c22">
<value val="12.0"/>
<symbolic val="true" />
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
</element>
<expression label="c13" exp="(a11 * p) + (a12 * q)" />
<element type="numeric" label="c13">
<value val="19.0"/>
<symbolic val="true" />
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
<algebra labelVisible="false"/></element>
<expression label="text18" exp=""" + (LaTeX[c11]) + """ />
<element type="text" label="text18">
<show object="true" label="false" ev="4"/>
<condition showObject="t ≥ 6"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<algebra labelVisible="false"/> <isLaTeX val="true"/>
<font serif="true" sizeM="2.0" size="20" style="1"/>
<startPoint exp="S"/>
<labelOffset x="-31" y="33"/>
</element>
<expression label="text19" exp=""" + (LaTeX[c12]) + """ />
<element type="text" label="text19">
<show object="true" label="false" ev="4"/>
<condition showObject="t ≥ 12"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<algebra labelVisible="false"/> <isLaTeX val="true"/>
<font serif="true" sizeM="2.0" size="20" style="1"/>
<startPoint exp="V"/>
<labelOffset x="-25" y="31"/>
</element>
<expression label="text20" exp=""" + (LaTeX[c13]) + """ />
<element type="text" label="text20">
<show object="true" label="false" ev="4"/>
<condition showObject="t ≥ 18"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<algebra labelVisible="false"/> <isLaTeX val="true"/>
<font serif="true" sizeM="2.0" size="20" style="1"/>
<startPoint exp="W"/>
<labelOffset x="-11" y="-12"/>
</element>
<expression label="text21" exp=""" + (LaTeX[c21]) + """ />
<element type="text" label="text21">
<show object="true" label="false" ev="4"/>
<condition showObject="t ≥ 24"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<algebra labelVisible="false"/> <isLaTeX val="true"/>
<font serif="true" sizeM="2.0" size="20" style="1"/>
<startPoint exp="T"/>
<labelOffset x="-3" y="-6"/>
</element>
<expression label="c23" exp="(b11 * p) + (b12 * q)" />
<element type="numeric" label="c23">
<value val="12.0"/>
<symbolic val="true" />
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
</element>
<expression label="text22" exp=""" + (LaTeX[c22]) + """ />
<element type="text" label="text22">
<show object="true" label="false" ev="4"/>
<condition showObject="t ≥ 30"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<algebra labelVisible="false"/> <isLaTeX val="true"/>
<font serif="true" sizeM="2.0" size="20" style="1"/>
<startPoint exp="U"/>
<labelOffset x="-29" y="25"/>
</element>
<expression label="text23" exp=""" + (LaTeX[c23]) + """ />
<element type="text" label="text23">
<show object="true" label="false" ev="4"/>
<condition showObject="t ≥ 36"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<algebra labelVisible="false"/> <isLaTeX val="true"/>
<font serif="true" sizeM="2.0" size="20" style="1"/>
<startPoint exp="Z"/>
<labelOffset x="-12" y="25"/>
</element>
<expression label="text9" exp=""" + (LaTeX[v]) + """ />
<element type="text" label="text9">
<show object="true" label="false" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0.0" dynamicr="0" dynamicg="0" dynamicb="If[Mod[t, 18] ≥ 9 ∧ Mod[t, 18] ≤ 12, 1, 0]" colorSpace="0"/>
<layer val="0"/>
<labelMode val="0"/>
<algebra labelVisible="false"/> <isLaTeX val="true"/>
<font serif="true" sizeM="2.0" size="20" style="1"/>
<startPoint exp="G"/>
<labelOffset x="-23" y="-34"/>
</element>
<expression label="text10" exp=""" + (LaTeX[q]) + """ />
<element type="text" label="text10">
<show object="true" label="false" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0.0" dynamicr="0" dynamicg="0" dynamicb="If[Mod[t, 18] ≥ 15 ∨ Mod[t, 18] ≟ 0, 1, 0]" colorSpace="0"/>
<layer val="0"/>
<labelMode val="0"/>
<algebra labelVisible="false"/> <isLaTeX val="true"/>
<font serif="true" sizeM="2.0" size="20" style="1"/>
<startPoint exp="J"/>
<labelOffset x="-28" y="-33"/>
</element>
<expression label="text24" exp=""({\red " + (LaTeX[a11]) + "})({\blue " + (LaTeX[m]) + "})+({\red " + (LaTeX[a12]) + "})({\blue " + (LaTeX[n]) + "})"" />
<element type="text" label="text24">
<show object="true" label="false" ev="4"/>
<condition showObject="t ≟ 5 ∨ t ≟ 6"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<algebra labelVisible="false"/> <isLaTeX val="true"/>
<font serif="true" sizeM="1.0" size="0" style="1"/>
<startPoint exp="M"/>
<labelOffset x="-37" y="-12"/>
</element>
<expression label="text26" exp=""(\red{" + (LaTeX[a11]) + "})(\blue{" + (LaTeX[p]) + "})+(\red{" + (LaTeX[a12]) + "})(\blue{" + (LaTeX[q]) + "})"" />
<element type="text" label="text26">
<show object="true" label="false" ev="4"/>
<condition showObject="t ≟ 17 ∨ t ≟ 18"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<algebra labelVisible="false"/> <isLaTeX val="true"/>
<font serif="true" sizeM="1.0" size="0" style="1"/>
<startPoint exp="Q"/>
<labelOffset x="-35" y="-16"/>
</element>
<expression label="text25" exp=""(\red{" + (LaTeX[a11]) + "})(\blue{" + (LaTeX[s]) + "})+(\red{" + (LaTeX[a12]) + "})(\blue{" + (LaTeX[v]) + "})"" />
<element type="text" label="text25">
<show object="true" label="false" ev="4"/>
<condition showObject="t ≟ 11 ∨ t ≟ 12"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<algebra labelVisible="false"/> <isLaTeX val="true"/>
<font serif="true" sizeM="1.0" size="0" style="1"/>
<startPoint exp="P"/>
<labelOffset x="-77" y="-21"/>
</element>
<expression label="text27" exp=""(\red{" + (LaTeX[b11]) + "})(\blue{" + (LaTeX[m]) + "})+(\red{" + (LaTeX[b12]) + "})(\blue{" + (LaTeX[n]) + "})"" />
<element type="text" label="text27">
<show object="true" label="false" ev="4"/>
<condition showObject="t ≟ 23 ∨ t ≟ 24"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<algebra labelVisible="false"/> <isLaTeX val="true"/>
<font serif="true" sizeM="1.0" size="0" style="1"/>
<startPoint exp="N"/>
<labelOffset x="-33" y="-4"/>
</element>
<expression label="text28" exp=""(\red{" + (LaTeX[b11]) + "})(\blue{" + (LaTeX[s]) + "})+(\red{" + (LaTeX[b12]) + "})(\blue{" + (LaTeX[v]) + "})"" />
<element type="text" label="text28">
<show object="true" label="false" ev="4"/>
<condition showObject="t ≟ 29 ∨ t ≟ 30"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<algebra labelVisible="false"/> <isLaTeX val="true"/>
<font serif="true" sizeM="1.0" size="0" style="1"/>
<startPoint exp="O"/>
<labelOffset x="-62" y="-16"/>
</element>
<expression label="text29" exp=""(\red{" + (LaTeX[b11]) + "})(\blue{" + (LaTeX[p]) + "})+(\red{" + (LaTeX[b12]) + "})(\blue{" + (LaTeX[q]) + "})"" />
<element type="text" label="text29">
<show object="true" label="false" ev="4"/>
<condition showObject="t ≟ 36 ∨ t ≟ 35"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<algebra labelVisible="false"/> <isLaTeX val="true"/>
<font serif="true" sizeM="1.0" size="0" style="1"/>
<startPoint exp="R"/>
<labelOffset x="-78" y="-16"/>
</element>
<element type="button" label="button2">
<show object="true" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelOffset x="868" y="340"/>
<labelMode val="0"/>
<fixed val="true"/>
<auxiliary val="true"/>
<ggbscript val="UpdateConstruction[]"/>
<font serif="false" sizeM="2.0" size="20" style="0"/>
<caption val="更换数据"/>
</element>
</construction>
</geogebra>