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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-CRS.xml

@@ -1190,6 +1190,7 @@
     </subsection>
     <reading-questions xml:id="readingquestions-CRS">
         <exercise xml:id="reading-CRS-1">
+            <title>Span of a column space</title>
             <statement>
                 <p>Write the column space of the matrix below as the span of a set of three vectors and explain your choice of method.<me>\begin{bmatrix}
                 1 &amp; 3 &amp; 1 &amp; 3\\
@@ -1199,11 +1200,13 @@
             </statement>
         </exercise>
         <exercise xml:id="reading-CRS-2">
+            <title>Column space of a nonsingular matrix</title>
             <statement>
                 <p>Suppose that <m>A</m> is an <m>n\times n</m> nonsingular matrix. What can you say about its column space?</p>
             </statement>
         </exercise>
         <exercise xml:id="reading-CRS-3">
+            <title>Vector in row space?</title>
             <statement>
                 <p> Is the vector <m>\colvector{0\\5\\2\\3}</m> in the row space of the following matrix?  Why or why not?<me>\begin{bmatrix}
                 1 &amp; 3 &amp; 1 &amp; 3\\

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-FS.xml

@@ -989,6 +989,7 @@
     </subsection>
     <reading-questions xml:id="readingquestions-FS">
         <exercise xml:id="reading-FS-1">
+            <title>Calculate element of left null space</title>
             <statement>
                 <p>Find a nontrivial element of the left null space of <m>A</m>.<me>A=
                 \begin{bmatrix}
@@ -999,6 +1000,7 @@
             </statement>
         </exercise>
         <exercise xml:id="reading-FS-2">
+            <title>Calculate parts of extended echelon form</title>
             <statement>
                 <p>Find the matrices <m>C</m> and <m>L</m> in the extended echelon form of <m>A</m>.<me>A=
                 \begin{bmatrix}
@@ -1009,6 +1011,7 @@
             </statement>
         </exercise>
         <exercise xml:id="reading-FS-3">
+            <title>Significance of Theorem FS</title>
             <statement>
                 <p> Why is <xref ref="theorem-FS" acro="FS"/> a great conclusion to <xref ref="chapter-M" acro="M"/>?</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-MINM.xml

@@ -591,6 +591,7 @@
     </subsection>
     <reading-questions xml:id="readingquestions-MINM">
         <exercise xml:id="reading-MINM-1">
+            <title>Calculate inverse, solve system</title>
             <statement>
                 <p>Compute the inverse of the coefficient matrix of the system of equations below and use the inverse to solve the system.<md>
                     <mrow>4x_1 + 10x_2 &amp;= 12</mrow>
@@ -599,6 +600,7 @@
             </statement>
         </exercise>
         <exercise xml:id="reading-MINM-2">
+            <title>Inverse doesn't exist</title>
             <statement>
                 <p>In the reading questions for <xref ref="section-MISLE" acro="MISLE"/> you were asked to find the  inverse of the <m>3\times 3</m> matrix below.<me>\begin{bmatrix}
                 2 &amp; 3 &amp; 1\\
@@ -608,6 +610,7 @@
             </statement>
         </exercise>
         <exercise xml:id="reading-MINM-3">
+            <title>Unitary or not</title>
             <statement>
                 <p>Is the matrix <m>A</m> unitary?  Why?<me>A=\begin{bmatrix}
                 \frac{1}{\sqrt{22}}\left(4+2i\right) &amp; \frac{1}{\sqrt{374}}\left(5+3i\right) \\

src2/section-MISLE.xml

@@ -775,6 +775,7 @@
     <!--   End  misle.tex -->
     <reading-questions xml:id="readingquestions-MISLE">
         <exercise xml:id="reading-MISLE-1">
+            <title>Calculate inverse of a <m>2\times 2</m> matrix</title>
             <statement>
                 <p>Compute the inverse of the matrix below.<me>\begin{bmatrix}
                 -2 &amp; 3\\
@@ -783,6 +784,7 @@
             </statement>
         </exercise>
         <exercise xml:id="reading-MISLE-2">
+            <title>Calculate inverse of a <m>3\times 3</m> matrix</title>
             <statement>
                 <p>Compute the inverse of the matrix below.<me>\begin{bmatrix}
                 2 &amp; 3 &amp; 1\\
@@ -792,6 +794,7 @@
             </statement>
         </exercise>
         <exercise xml:id="reading-MISLE-3">
+            <title>Title of Theorem SS</title>
             <statement>
                 <p> Explain why <xref ref="theorem-SS" acro="SS"/> has the title it does. (Do not just state the theorem, explain the choice of the title making reference to the theorem itself.)</p>
             </statement>

src2/section-MM.xml

@@ -960,6 +960,7 @@
     </subsection>
     <reading-questions xml:id="readingquestions-MM">
         <exercise xml:id="reading-MM-1">
+            <title>Matrix-vector product</title>
             <statement>
                 <p>Form the matrix-vector product of<md>
                     <mrow>\begin{bmatrix}
@@ -973,6 +974,7 @@
             </statement>
         </exercise>
         <exercise xml:id="reading-MM-2">
+            <title>Calculate product of two matrices</title>
             <statement>
                 <p> Multiply together the two matrices below (in the order given).<md>
                     <mrow>\begin{bmatrix}
@@ -991,6 +993,7 @@
             </statement>
         </exercise>
         <exercise xml:id="reading-MM-3">
+            <title>Matrix-vector product form of a linear system</title>
             <statement>
                 <p>Rewrite the system of linear equations below as a vector equality and using a matrix-vector product.  (This question does not ask for a solution to the system.  But it does ask you to express the system of equations in a new form using tools from this section.)<md>
                     <mrow>2x_1 + 3x_2 - x_3 &amp;= 0</mrow>

src2/section-MO.xml

@@ -922,6 +922,7 @@
     </subsection>
     <reading-questions xml:id="readingquestions-MO">
         <exercise xml:id="reading-MO-1">
+            <title>Calculate sum and scalar mult of matrices</title>
             <statement>
                 <p>Perform the following matrix computation.<me>(6)
                 \begin{bmatrix}
@@ -939,11 +940,13 @@
             </statement>
         </exercise>
         <exercise xml:id="reading-MO-2">
+            <title>Vector space of matrices</title>
             <statement>
                 <p><xref ref="theorem-VSPM" acro="VSPM"/> reminds you of what previous theorem? How strong is the similarity?</p>
             </statement>
         </exercise>
         <exercise xml:id="reading-MO-3">
+            <title>Calculate transpose</title>
             <statement>
                 <p>Compute the transpose of the matrix below.<me>\begin{bmatrix}
                 6 &amp; 8 &amp; 4 \\

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>