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2 changes: 1 addition & 1 deletion requirements.txt
Original file line number Diff line number Diff line change
@@ -1,5 +1,5 @@
pretext[prefigure] == 2.36.0
prefig >= 0.5.7
prefig >= 0.5.15
CodeChat-Server == 0.2.25
pelican == 4.11.0
markdown == 3.7.0
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35 changes: 15 additions & 20 deletions source/linear-algebra/source/04-MX/01.ptx
Original file line number Diff line number Diff line change
Expand Up @@ -367,30 +367,25 @@ in terms of matrix multiplication.</p>
</ul>
</statement>
</exploration>
<exploration>
<statement>
<p>Use the included map in this problem.</p>
<figure xml:id="MX1-adjacency">
<caption>Adjacency map, showing roads between 5 cities</caption>
<image xml:id="MX1-image-adjacency" width="50%">
<description>A map with 5 dots. A is connected to B, B is connected to C, C is connected to D and E, and D and E are connected to each other</description>
<latex-image>
\tikz{\node[shape=circle,draw=black] (A) at (0,0) {A};
\node[shape=circle,draw=black] (B) at (0,2) {B};
\node[shape=circle,draw=black] (C) at (0,4) {C};
\node[shape=circle,draw=black] (D) at (-2,6) {D};
\node[shape=circle,draw=black] (E) at (2,6) {E};
\draw (A)--(B)--(C)--(D)--(E)--(C)}
</latex-image>
</image>
</figure>
<exploration>
<statement>
<p>Use the included map in this problem.</p>
<figure xml:id="MX1-adjacency">
<caption>Adjacency map, showing roads between 5 cities</caption>
<image>
<description>A map with 5 dots. A is connected to B, B is connected to C, C is connected to D and E, and D and E are connected to each other</description>
<prefigure xmlns="https://prefigure.org" label="prefigure-MX1-graph">
<xi:include href="prefigure/MX1-adjacency-graph.xml"/>
</prefigure>
</image>
</figure>

<ul>
<li>An <em>adjacency matrix</em> for this map is a matrix that has the number of roads from city <m>i</m> to city <m>j</m> in the <m>(i,j)</m> entry of the matrix. A road is a path of length exactly 1. All <m>(i,i)</m>entries are 0. Write the adjacency matrix for this map, with the cities in alphabetical order.</li>

<li>What does the square of this matrix tell you about the map? The cube? The <m>n</m>-th power?</li>
</ul>
</statement>
<li>What does the square of this matrix tell you about the map? The cube? The <m>n</m>-th power?</li>
</ul>
</statement>
</exploration>
</subsection>
<subsection component="html">
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Original file line number Diff line number Diff line change
@@ -0,0 +1,37 @@
<diagram dimensions="(600,300)" margins="5" xmlns="https://prefigure.org">
<coordinates bbox="(-1,-0.5,1,0.5)">
<network scale="0.8" node-fill="#ccf" node-stroke="black"
seed="1" labels="yes" layout="bfs" start="0"
tactile-node-size="40">
<node at="0">A</node>
<node at="1">B</node>
<node at="2">C</node>
<node at="3">D</node>
<node at="4">E</node>
<edge vertices="[0,1]"/>
<edge vertices="[1,2]"/>
<edge vertices="[2,3]"/>
<edge vertices="[2,4]"/>
<edge vertices="[3,4]"/>
</network>
</coordinates>

<annotations>
<annotation ref="figure" text="A network with five vertices">
<annotation ref="node-0" text="The node labeled A">
<annotation ref="edge-0-1" text="An edge connecting A and B"/>
</annotation>
<annotation ref="node-1" text="The node labeled B">
<annotation ref="edge-1-2" text="An edge connecting B and C"/>
</annotation>
<annotation ref="node-2" text="The node labeled C">
<annotation ref="edge-2-3" text="An edge connecting C and D"/>
<annotation ref="edge-2-4" text="An edge connecting C and E"/>
</annotation>
<annotation ref="node-3" text="The node labeled D">
<annotation ref="edge-3-4" text="An edge connecting D and E"/>
</annotation>
<annotation ref="node-4" text="The node labeled E"/>
</annotation>
</annotations>
</diagram>
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