Add titles to reading questions in Chapter V (PR #101)

src2/section-LC.xml

@@ -1094,6 +1094,7 @@
     </subsection>
     <reading-questions xml:id="readingquestions-LC">
         <exercise xml:id="reading-LC-1">
+            <title>Write linear system as vector equality</title>
             <statement>
                 <p>Earlier, a reading question asked you to solve the system of equations<md>
                     <mrow>2x_1 + 3x_2 - x_3&amp;= 0</mrow>
@@ -1103,11 +1104,13 @@
             </statement>
         </exercise>
         <exercise xml:id="reading-LC-2">
+            <title>Calculate linear combination equal to vector</title>
             <statement>
                 <p>Find a linear combination of the vectors<me>S=\set{\colvector{1\\3\\-1},\,\colvector{2\\0\\4},\,\colvector{-1\\3\\-5}}</me>that equals the vector <m>\colvector{1\\-9\\11}</m>.</p>
             </statement>
         </exercise>
         <exercise xml:id="reading-LC-3">
+            <title>Calculate vector form of a solution set</title>
             <statement>
                 <p>The matrix below is the augmented matrix of a system of equations, row-reduced to reduced row-echelon form.  Write the vector form of the solutions to the system.<me>\begin{bmatrix}
                  \leading{1}&amp;3&amp;0&amp;6&amp;0&amp;9\\

src2/section-LDS.xml

@@ -676,16 +676,19 @@
     </subsection>
     <reading-questions xml:id="readingquestions-LDS">
         <exercise xml:id="reading-LDS-1">
+            <title>Caclulate linear combination from dependent set</title>
             <statement>
                 <p>Let  <m>S</m>  be the linearly dependent set of three vectors below.<me>S=\set{\colvector{1\\10\\100\\1000},\,\colvector{1\\1\\1\\1},\,\colvector{5\\23\\203\\2003}}</me>Write one vector from <m>S</m> as a linear combination of the other two and include this vector equality in your response.  (You should be able to do this on sight, rather than doing some computations.)  Convert this expression into a nontrivial relation of linear dependence on <m>S</m>.</p>
             </statement>
         </exercise>
         <exercise xml:id="reading-LDS-2">
+            <title>"Dependent" in definition of linear dependence</title>
             <statement>
                 <p> Explain why the word <q>dependent</q> is used in the definition of linear dependence.</p>
             </statement>
         </exercise>
         <exercise xml:id="reading-LDS-3">
+            <title>Prefer linearly dependent spanning set?</title>
             <statement>
                 <p>Suppose that <m>Y=\spn{P}=\spn{Q}</m>, where <m>P</m> is a linearly dependent set and <m>Q</m> is linearly independent.  Would you rather use <m>P</m> or <m>Q</m> to describe <m>Y</m>?  Why?</p>
             </statement>

src2/section-LI.xml

@@ -571,16 +571,19 @@
     </subsection>
     <reading-questions xml:id="readingquestions-LI">
         <exercise xml:id="reading-LI-1">
+            <title>Is a set linearly independent?</title>
             <statement>
                 <p>Let  <m>S</m>  be the set of three vectors below.<me>S=\set{\colvector{1\\2\\-1},\,\colvector{3\\-4\\2},\,\colvector{4\\-2\\1}}</me>Is <m>S</m> linearly independent or linearly dependent?  Explain why.</p>
             </statement>
         </exercise>
         <exercise xml:id="reading-LI-2">
+            <title>Is another set linearly independent?</title>
             <statement>
                 <p> Let <m>S</m> be the set of three vectors below.<me>S=\set{\colvector{1\\-1\\0},\,\colvector{3\\2\\2},\,\colvector{4\\3\\-4}}</me>Is <m>S</m> linearly independent or linearly dependent?  Explain why.</p>
             </statement>
         </exercise>
         <exercise xml:id="reading-LI-3">
+            <title>Connect linear (in)dependence to (non)singularity</title>
             <statement>
                 <p>Is the matrix below singular or nonsingular?  Explain your answer using only the final conclusion you reached in the previous question, along with one new theorem.<me>\begin{bmatrix}
                  1  &amp;3  &amp;4\\

src2/section-O.xml

@@ -886,16 +886,19 @@
     </subsection>
     <reading-questions xml:id="readingquestions-O">
         <exercise xml:id="reading-O-1">
+            <title>Given set orthogonal?</title>
             <statement>
                 <p>Is the set<me>\set{\colvector{1\\-1\\2},\,\colvector{5\\3\\-1},\,\colvector{8\\4\\-2}}</me>an orthogonal set?  Why?</p>
             </statement>
         </exercise>
         <exercise xml:id="reading-O-2">
+            <title>Orthogonal vs orthonormal</title>
             <statement>
                 <p>What is the distinction between an orthogonal set and an orthonormal set?</p>
             </statement>
         </exercise>
         <exercise xml:id="reading-O-3">
+            <title>Output of Gram-Schmidt process</title>
             <statement>
                 <p> What is nice about the output of the Gram-Schmidt process?</p>
             </statement>

src2/section-SS.xml

@@ -769,16 +769,19 @@
     <!--   End  ss.tex -->
     <reading-questions xml:id="readingquestions-SS">
         <exercise xml:id="reading-SS-1">
+            <title>Is vector in span?</title>
             <statement>
                 <p>Let  S  be the set of three vectors below.<me>S=\set{\colvector{1\\2\\-1},\,\colvector{3\\-4\\2},\,\colvector{4\\-2\\1}}</me>.  Let <m>W=\spn{S}</m> be the span of  S. Is the vector <m>\colvector{-1\\8\\-4}</m> in <m>W</m>?  Give an explanation of the reason for your answer.</p>
             </statement>
         </exercise>
         <exercise xml:id="reading-SS-2">
+            <title>Another is vector in span?</title>
             <statement>
                 <p>Use  <m>S</m> and <m>W</m>  from the previous question.  Is the vector <m>\colvector{6\\5\\-1}</m> in <m>W</m>?  Give an explanation of the reason for your answer.</p>
             </statement>
         </exercise>
         <exercise xml:id="reading-SS-3">
+            <title>Calculate spanning set of a null space</title>
             <statement>
                 <p>For the matrix <m>A</m> below, find a set <m>S</m> so that <m>\spn{S}=\nsp{A}</m>, where <m>\nsp{A}</m> is the null space of <m>A</m>.  (See <xref ref="theorem-SSNS" acro="SSNS"/>.)<me>A=
                 \begin{bmatrix}

src2/section-VO.xml

@@ -523,16 +523,19 @@
     </subsection>
     <reading-questions xml:id="readingquestions-VO">
         <exercise xml:id="reading-VO-1">
+            <title>Seen vectors before?</title>
             <statement>
                 <p> Where have you seen vectors used before in other courses?  How were they different?</p>
             </statement>
         </exercise>
         <exercise xml:id="reading-VO-2">
+            <title>Equality of vectors</title>
             <statement>
                 <p>In words only, when are two vectors equal?</p>
             </statement>
         </exercise>
         <exercise xml:id="reading-VO-3">
+            <title>Calculate scalar multiplication and adding vectors</title>
             <statement>
                 <p>Perform the following computation with vector operations<me>2\colvector{1\\5\\0} + (-3)\colvector{7\\6\\5}</me></p>
             </statement>