Add titles to reading questions for Chapter VS (PR #102)

src2/section-B.xml

@@ -706,6 +706,7 @@
     <!--   End  b.tex -->
     <reading-questions xml:id="readingquestions-B">
         <exercise xml:id="reading-B-1">
+            <title>Columns of a nonsingular matrix</title>
             <statement>
                 <p>The matrix below is nonsingular.  What can you now say about its columns?<me>A=\begin{bmatrix}
                 -3 &amp; 0 &amp; 1\\
@@ -715,11 +716,13 @@
             </statement>
         </exercise>
         <exercise xml:id="reading-B-2">
+            <title>Linear combination of columns</title>
             <statement>
                 <p>Write the vector <m>\vect{w}=\colvector{6\\6\\15}</m> as a linear combination of the columns of the matrix <m>A</m> above.  How many ways are there to answer this question?</p>
             </statement>
         </exercise>
         <exercise xml:id="reading-B-3">
+            <title>Why desire orthonormal?</title>
             <statement>
                 <p>Why is an orthonormal basis desirable?</p>
             </statement>

src2/section-D.xml

@@ -568,16 +568,19 @@
     </subsection>
     <reading-questions xml:id="readingquestions-D">
         <exercise xml:id="reading-D-1">
+            <title>Calculate dimension of <m>P_6</m></title>
             <statement>
                 <p>What is the dimension of the vector space <m>P_6</m>, the set of all polynomials of degree 6 or less?</p>
             </statement>
         </exercise>
         <exercise xml:id="reading-D-2">
+            <title>Relate rank and nullity</title>
             <statement>
                 <p>How are the rank and nullity of a matrix related?</p>
             </statement>
         </exercise>
         <exercise xml:id="reading-D-3">
+            <title>Rank of a nonsingular matrix</title>
             <statement>
                 <p>Explain why we might say that a nonsingular matrix has <q>full rank.</q></p>
             </statement>

src2/section-LISS.xml

@@ -435,6 +435,7 @@
     <!--   End  liss.tex -->
     <reading-questions xml:id="readingquestions-LISS">
         <exercise xml:id="reading-LISS-1">
+            <title>Linear dependence of set of matrices</title>
             <statement>
                 <p>Is the set of matrices below linearly independent or linearly dependent in the vector space <m>M_{22}</m>?  Why or why not?<me>\set{
                 \begin{bmatrix}
@@ -450,6 +451,7 @@
             </statement>
         </exercise>
         <exercise xml:id="reading-LISS-2">
+            <title>Span vs. spans</title>
             <statement>
                 <p>Explain the difference between the following two uses of the term <q>span</q>:<ol>
                     <li><m>S</m> is a subset of the vector space <m>V</m> and the span of <m>S</m> is a subspace of <m>V</m>.</li>
@@ -458,6 +460,7 @@
             </statement>
         </exercise>
         <exercise xml:id="reading-LISS-3">
+            <title>Linear combination of vectors in linearly independent set</title>
             <statement>
                 <p>The set<me>S=\set{
                 \colvector{6\\2\\1},\,

src2/section-PD.xml

@@ -378,16 +378,19 @@
     </subsection>
     <reading-questions xml:id="readingquestions-PD">
         <exercise xml:id="reading-PD-1">
+            <title>Title of Theorem G</title>
             <statement>
                 <p>Why does <xref ref="theorem-G" acro="G"/> have the title it does?</p>
             </statement>
         </exercise>
         <exercise xml:id="reading-PD-2">
+            <title>Theorem RMRT surprising</title>
             <statement>
                 <p>Why is <xref ref="theorem-RMRT" acro="RMRT"/> so surprising ?</p>
             </statement>
         </exercise>
         <exercise xml:id="reading-PD-3">
+            <title>Calculate dimensions of the 4 subspaces</title>
             <statement>
                 <p>Row-reduce the matrix <m>A</m> to reduced row-echelon form.  Without any further computations, compute the dimensions of the four subspaces, (a) <m>\nsp{A}</m>, (b) <m>\csp{A}</m>, (c) <m>\rsp{A}</m>  and  (d) <m>\lns{A}</m>.<me>A=
                 \begin{bmatrix}

src2/section-S.xml

@@ -707,16 +707,19 @@
     </subsection>
     <reading-questions xml:id="readingquestions-S">
         <exercise xml:id="reading-S-1">
+            <title>Subspace test</title>
             <statement>
                 <p>Summarize the three conditions that allow us to quickly test if a set is a subspace.</p>
             </statement>
         </exercise>
         <exercise xml:id="reading-S-2">
+            <title>Apply the subspace test</title>
             <statement>
                 <p>Consider the set of vectors<me>W=\setparts{\colvector{a\\b\\c}}{3a-2b+c=5}</me>.  Is the set <m>W</m> a subspace of <m>\complex{3}</m>?  Explain your answer.</p>
             </statement>
         </exercise>
         <exercise xml:id="reading-S-3">
+            <title>Name five subspaces</title>
             <statement>
                 <p>Name five general constructions of sets of column vectors (subsets of <m>\complex{m}</m>) that we now know as subspaces.</p>
             </statement>

src2/section-VS.xml

@@ -553,16 +553,19 @@
     </subsection>
     <reading-questions xml:id="readingquestions-VS">
         <exercise xml:id="reading-VS-1">
+            <title>Complex vector space</title>
             <statement>
                 <p>Comment on how the vector space <m>\complex{m}</m> went from a theorem (<xref ref="theorem-VSPCV" acro="VSPCV"/>) to an example (<xref ref="example-VSCV" acro="VSCV"/>).</p>
             </statement>
         </exercise>
         <exercise xml:id="reading-VS-2">
+            <title>Calculate linear combination in Crazy Vector Space</title>
             <statement>
                 <p>In the crazy vector space, <m>C</m>, (<xref ref="example-CVS" acro="CVS"/>) compute the linear combination<me>2(3,\,4)+(-6)(1,\,2)</me>.</p>
             </statement>
         </exercise>
         <exercise xml:id="reading-VS-3">
+            <title>Why prove things about the zero vector?</title>
             <statement>
                 <p>Suppose that <m>\alpha</m> is a scalar and <m>\zerovector</m> is the zero vector. Why should we prove anything as obvious as <m>\alpha\zerovector=\zerovector</m> such as we did in <xref ref="theorem-ZVSM" acro="ZVSM"/>?</p>
             </statement>