Chapter 2 proofreading fixes

source/linear-algebra/source/02-EV/03.ptx

@@ -343,7 +343,7 @@ we'll learn what this means more carefully in a later chapter.
         </p>
         <figure xml:id="EV3-planar-subspace-vs-r2">
 			<caption>A planar subset of <m>\IR^3</m> compared with the plane <m>\IR^2</m>.</caption>
-            <sidebyside>
+            <sidebyside component="html">
                 <image xml:id="EV3-image-r2-in-r3">
                     <description><p>A planar subset of <m>\IR^3</m>.</p></description>
                     <sageplot variant="3d" aspect="1.0">
@@ -362,6 +362,18 @@ p += plot(vector([3,-1]), color="yellow")
 p
                     </sageplot>
                 </image>
+            </sidebyside>
+            <sidebyside component="print">
+                <image>
+                    <prefigure xmlns="https://prefigure.org" label="prefigure-EV3-planar-subset">
+                        <xi:include href="prefigure/EV3-planar-subset.xml"/>
+                    </prefigure>
+                </image>
+                <image>
+                    <prefigure xmlns="https://prefigure.org" label="prefigure-EV3-R2">
+                        <xi:include href="prefigure/EV3-R2.xml"/>
+                    </prefigure>
+                </image>
             </sidebyside>
 		</figure>
 </observation>
@@ -1108,7 +1120,7 @@ that is, <m>(kx)+(ky)=(kx)(ky)</m>. This is verified by the following calculatio
                 <p>
                     A square matrix <m>M</m> is <term>symmetric</term><idx>symmetric matrix</idx> if, for each index <m>i,j</m>, the entries <m>m_{ij} = m_{ji}</m>. That is, the matrix is itself when reflected over the diagonal from upper left to lower right.
 
-Prove that the set of <m>n \times n</m> symmetric matrices is a subspace of <m>M_{n \times n}</m>.
+Prove that the set of <m>n \times n</m> symmetric matrices is a subspace of <m>M_{n,n}</m>.
                 </p>
     </exploration>
     <exploration>
@@ -1124,7 +1136,7 @@ Decide if each of the following is a subspace. If so, prove it. If not, provide
 <exploration>
     <p>
 Give an example of each of these, or explain why it's not possible that such a thing would exist.
-<ul> <li>A nonempty subset of <m>M_{2 \times 2}</m> that is not a subspace.</li>
+<ul> <li>A nonempty subset of <m>M_{2,2}</m> that is not a subspace.</li>
 <li> A set of two vectors in <m>\mathbb{R}^2</m> that is not a spanning set.</li>
 </ul>
 </p></exploration>

source/linear-algebra/source/02-EV/04.ptx

@@ -664,7 +664,7 @@ vectors that can form a linearly independent set?
     <title>Mathematical Writing Explorations</title>
             <exploration>
                 <p>
-                    Prove the result of <xref ref="def_of_LI"></xref>, by showing that, given a set <m>S = \{\vec{v}_1,\vec{v}_2,\ldots,\vec{v}_n\}</m> of vectors, <m>S</m> is linearly independent iff the equation <m>x_1\vec{v}_1 + x_2\vec{v}_2 + \ldots\ + x_n\vec{v}_n = \vec{0}</m> is only true when <m>x_1 = x_2 = \cdots = x_n = 0</m>. 
+                    Prove the result of <xref ref="def_of_LI"></xref>, by showing that, given a set <m>S = \{\vec{v}_1,\vec{v}_2,\ldots,\vec{v}_n\}</m> of vectors, <m>S</m> is linearly independent if and only f the equation <m>x_1\vec{v}_1 + x_2\vec{v}_2 + \ldots\ + x_n\vec{v}_n = \vec{0}</m> is only true when <m>x_1 = x_2 = \cdots = x_n = 0</m>. 
                 </p>
     </exploration>
     </subsection>

source/linear-algebra/source/02-EV/prefigure/EV3-R2.xml

@@ -0,0 +1,10 @@
+<diagram dimensions="(300,300)" margins="5" xmlns="https://prefigure.org">
+  <coordinates bbox="(-6,-6,6,6)">
+    <polygon points="((-5,-5),(-5,5),(5,5),(5,-5))" closed="yes"
+             fill="cyan"/>
+    <line endpoints="(-5,0),(5,0)" arrows="2" stroke="gray" opacity="0.5" thickness="1"/>
+    <line endpoints="(0,-5),(0,5)" arrows="21" stroke="gray" opacity="0.5" thickness="1"/>
+    <vector v="(3,-1)" stroke="yellow"/>
+    <vector v="(1,2)" stroke="purple"/>
+  </coordinates>
+</diagram>

source/linear-algebra/source/02-EV/prefigure/EV3-planar-subset.xml

@@ -0,0 +1,11 @@
+<diagram dimensions="(300,300)" margins="5" xmlns="https://prefigure.org">
+  <coordinates bbox="(-6,-6,6,6)">
+    <polygon points="((-3,-3),(-5,4),(3,5),(5,-2))" closed="yes"
+             fill="cyan"/>
+    <line endpoints="(0,0),(5,0)" arrows="1" stroke="gray" opacity="0.5" thickness="1"/>
+    <line endpoints="(0,0),(0,5)" arrows="1" stroke="gray" opacity="0.5" thickness="1"/>
+    <line endpoints="(0,0),(4.2*cos(7*pi/6),4.2*sin(7*pi/6))" arrows="1" stroke="gray" opacity="0.5" thickness="1"/>
+    <vector v="(-2,1)" stroke="yellow"/>
+    <vector v="(-1,-2.5)" stroke="purple"/>
+  </coordinates>
+</diagram>