From b53975d917a3cc20e497f2cef4213c88ca2068fd Mon Sep 17 00:00:00 2001 From: Drew Lewis Date: Fri, 8 May 2026 22:25:18 +0000 Subject: [PATCH 1/2] Tweak sample exercises --- .../source/01-LE/samples/01.ptx | 7 +- .../source/01-LE/samples/02.ptx | 6 +- .../source/01-LE/samples/03.ptx | 6 +- .../source/01-LE/samples/04.ptx | 6 +- .../source/02-EV/samples/01.ptx | 6 +- .../source/02-EV/samples/02.ptx | 6 +- .../source/02-EV/samples/03.ptx | 6 +- .../source/02-EV/samples/04.ptx | 6 +- .../source/02-EV/samples/05.ptx | 6 +- .../source/02-EV/samples/06.ptx | 6 +- .../source/02-EV/samples/07.ptx | 6 +- .../source/03-AT/samples/01.ptx | 6 +- .../source/03-AT/samples/02.ptx | 6 +- .../source/03-AT/samples/03.ptx | 6 +- .../source/03-AT/samples/04.ptx | 6 +- .../source/03-AT/samples/05.ptx | 6 +- .../source/03-AT/samples/06.ptx | 6 +- .../source/04-MX/samples/01.ptx | 6 +- .../source/04-MX/samples/02.ptx | 7 +- .../source/04-MX/samples/03.ptx | 6 +- .../source/04-MX/samples/04.ptx | 7 +- .../source/05-GT/samples/01.ptx | 6 +- .../source/05-GT/samples/02.ptx | 6 +- .../source/05-GT/samples/03.ptx | 7 +- .../source/05-GT/samples/04.ptx | 6 +- source/linear-algebra/source/meta/docinfo.ptx | 5 +- .../source/meta/sample-exercises.ptx | 65 ++++++++++++------- xsl/print.xsl | 19 ++++++ 28 files changed, 163 insertions(+), 80 deletions(-) diff --git a/source/linear-algebra/source/01-LE/samples/01.ptx b/source/linear-algebra/source/01-LE/samples/01.ptx index a558445ee..f39da7f6b 100644 --- a/source/linear-algebra/source/01-LE/samples/01.ptx +++ b/source/linear-algebra/source/01-LE/samples/01.ptx @@ -1,6 +1,7 @@ - - LE1 + + LE1 + <xref ref="LE1" text="global"/>

Consider the vector equation x_{1} \left[\begin{array}{c} 4 \\ -3 \\ 3 \end{array}\right] + x_{2} \left[\begin{array}{c} 4 \\ -3 \\ 3 \end{array}\right] + x_{3} \left[\begin{array}{c} 3 \\ 1 \\ 3 \end{array}\right] + x_{4} \left[\begin{array}{c} 18 \\ -7 \\ 15 \end{array}\right] = \left[\begin{array}{c} -11 \\ 5 \\ -9 \end{array}\right]

 @@ -34,4 +35,4 @@

- + diff --git a/source/linear-algebra/source/01-LE/samples/02.ptx b/source/linear-algebra/source/01-LE/samples/02.ptx index 8d3926237..17843d611 100644 --- a/source/linear-algebra/source/01-LE/samples/02.ptx +++ b/source/linear-algebra/source/01-LE/samples/02.ptx @@ -1,6 +1,8 @@ -LE2 + + LE2 + <xref ref="LE2" text="global"/>

For each of the following matrices, explain why it is not in reduced row echelon form.

@@ -107,4 +109,4 @@

- + diff --git a/source/linear-algebra/source/01-LE/samples/03.ptx b/source/linear-algebra/source/01-LE/samples/03.ptx index e97e10f1b..f86038d8c 100644 --- a/source/linear-algebra/source/01-LE/samples/03.ptx +++ b/source/linear-algebra/source/01-LE/samples/03.ptx @@ -1,5 +1,7 @@ -LE3 + + LE3 + <xref ref="LE3" text="global"/>

Consider each of the following systems of linear equations or vector equations.

@@ -130,4 +132,4 @@ - \ No newline at end of file + \ No newline at end of file diff --git a/source/linear-algebra/source/01-LE/samples/04.ptx b/source/linear-algebra/source/01-LE/samples/04.ptx index 8b44a514d..8bd70889c 100644 --- a/source/linear-algebra/source/01-LE/samples/04.ptx +++ b/source/linear-algebra/source/01-LE/samples/04.ptx @@ -1,5 +1,7 @@ -LE4 + + LE4 + <xref ref="LE4" text="global"/>

Consider the following vector equation. x_{1} \left[\begin{array}{c} 1 \\ 0 \\ 1 \\ 1 \end{array}\right] + x_{2} \left[\begin{array}{c} -2 \\ 0 \\ -2 \\ -2 \end{array}\right] + x_{3} \left[\begin{array}{c} -5 \\ 1 \\ -5 \\ -2 \end{array}\right] + x_{4} \left[\begin{array}{c} 13 \\ -2 \\ 13 \\ 7 \end{array}\right] + x_{5} \left[\begin{array}{c} -14 \\ 3 \\ -14 \\ -5 \end{array}\right] = \left[\begin{array}{c} 18 \\ -3 \\ 18 \\ 9 \end{array}\right]

@@ -47,4 +49,4 @@

Therefore, the solution set is \left\{ \left[\begin{array}{c} 2 \, a - 3 \, b - c + 3 \\ a \\ 2 \, b - 3 \, c - 3 \\ b \\ c \end{array}\right] \,\middle|\, a,b,c \in\mathbb R \right\}.

- \ No newline at end of file + \ No newline at end of file diff --git a/source/linear-algebra/source/02-EV/samples/01.ptx b/source/linear-algebra/source/02-EV/samples/01.ptx index d422dae8f..5403e37d6 100644 --- a/source/linear-algebra/source/02-EV/samples/01.ptx +++ b/source/linear-algebra/source/02-EV/samples/01.ptx @@ -1,5 +1,7 @@ -EV1 + + EV1 + <xref ref="EV1" text="global"/>

Consider each of these claims about a vector equation.

 @@ -97,4 +99,4 @@ x_4\left[\begin{array}{c} -5 \\ 1 \\ -5 \end{array}\right] = - \ No newline at end of file + \ No newline at end of file diff --git a/source/linear-algebra/source/02-EV/samples/02.ptx b/source/linear-algebra/source/02-EV/samples/02.ptx index 477f25bbb..77f7a6d79 100644 --- a/source/linear-algebra/source/02-EV/samples/02.ptx +++ b/source/linear-algebra/source/02-EV/samples/02.ptx @@ -1,5 +1,7 @@ -EV2 + + EV2 + <xref ref="EV2" text="global"/>

Consider the set of vectors \left\{ \left[\begin{array}{c} -1 \\ 1 \\ 0 \\ 2 \end{array}\right] , @@ -137,4 +139,4 @@ - + diff --git a/source/linear-algebra/source/02-EV/samples/03.ptx b/source/linear-algebra/source/02-EV/samples/03.ptx index ed94fc0e4..1a3e9377b 100644 --- a/source/linear-algebra/source/02-EV/samples/03.ptx +++ b/source/linear-algebra/source/02-EV/samples/03.ptx @@ -1,6 +1,8 @@ -EV3 + + EV3 + <xref ref="EV3" text="global"/>

Answer the following questions about Euclidean subspaces.

@@ -95,4 +97,4 @@

- \ No newline at end of file + \ No newline at end of file diff --git a/source/linear-algebra/source/02-EV/samples/04.ptx b/source/linear-algebra/source/02-EV/samples/04.ptx index a5500cf75..c03317cf2 100644 --- a/source/linear-algebra/source/02-EV/samples/04.ptx +++ b/source/linear-algebra/source/02-EV/samples/04.ptx @@ -1,6 +1,8 @@ -EV4 + + EV4 + <xref ref="EV4" text="global"/>

@@ -116,4 +118,4 @@ - \ No newline at end of file + \ No newline at end of file diff --git a/source/linear-algebra/source/02-EV/samples/05.ptx b/source/linear-algebra/source/02-EV/samples/05.ptx index 44f67d833..6dddf5297 100644 --- a/source/linear-algebra/source/02-EV/samples/05.ptx +++ b/source/linear-algebra/source/02-EV/samples/05.ptx @@ -1,5 +1,7 @@ -EV5 + + EV5 + <xref ref="EV5" text="global"/>

Consider the set of vectors \left\{ \left[\begin{array}{c} 1 \\ -2 \\ 0 \\ 1 \end{array}\right] , \left[\begin{array}{c} 2 \\ -4 \\ 0 \\ 2 \end{array}\right] , \left[\begin{array}{c} 3 \\ -6 \\ 0 \\ 3 \end{array}\right] , \left[\begin{array}{c} 5 \\ -5 \\ -2 \\ 4 \end{array}\right] \right\}

@@ -79,4 +81,4 @@ - + diff --git a/source/linear-algebra/source/02-EV/samples/06.ptx b/source/linear-algebra/source/02-EV/samples/06.ptx index f4f0c7e81..72537b13c 100644 --- a/source/linear-algebra/source/02-EV/samples/06.ptx +++ b/source/linear-algebra/source/02-EV/samples/06.ptx @@ -1,6 +1,8 @@ -EV6 + + EV6 + <xref ref="EV6" text="global"/>

Consider the subspace @@ -63,4 +65,4 @@ Since this (and thus every other) basis has three vectors in it, the dimension o

- + diff --git a/source/linear-algebra/source/02-EV/samples/07.ptx b/source/linear-algebra/source/02-EV/samples/07.ptx index f35c8e54c..4f5cb4359 100644 --- a/source/linear-algebra/source/02-EV/samples/07.ptx +++ b/source/linear-algebra/source/02-EV/samples/07.ptx @@ -1,6 +1,8 @@ -EV7 + + EV7 + <xref ref="EV7" text="global"/>

Consider the homogeneous system of equations @@ -86,4 +88,4 @@ a basis for the solution space is

- + diff --git a/source/linear-algebra/source/03-AT/samples/01.ptx b/source/linear-algebra/source/03-AT/samples/01.ptx index b20167a47..76757456b 100644 --- a/source/linear-algebra/source/03-AT/samples/01.ptx +++ b/source/linear-algebra/source/03-AT/samples/01.ptx @@ -1,6 +1,8 @@ -AT1 + + AT1 + <xref ref="AT1" text="global"/>

Answer the following questions about transformations.

    @@ -124,4 +126,4 @@

- \ No newline at end of file + \ No newline at end of file diff --git a/source/linear-algebra/source/03-AT/samples/02.ptx b/source/linear-algebra/source/03-AT/samples/02.ptx index 80bc912df..05ebe07b3 100644 --- a/source/linear-algebra/source/03-AT/samples/02.ptx +++ b/source/linear-algebra/source/03-AT/samples/02.ptx @@ -1,5 +1,7 @@ -AT2 + + AT2 + <xref ref="AT2" text="global"/>

    @@ -52,4 +54,4 @@ S\left(\left[\begin{array}{c} -2 \\ 1 \\ 3 \\ 2 \end{array}\right] \right) = -2S

- \ No newline at end of file + \ No newline at end of file diff --git a/source/linear-algebra/source/03-AT/samples/03.ptx b/source/linear-algebra/source/03-AT/samples/03.ptx index 1b94eac39..eeec4c57c 100644 --- a/source/linear-algebra/source/03-AT/samples/03.ptx +++ b/source/linear-algebra/source/03-AT/samples/03.ptx @@ -1,6 +1,8 @@ -AT3 + + AT3 + <xref ref="AT3" text="global"/>

Let T: \IR^4 \rightarrow \IR^3 be the linear transformation given by @@ -99,4 +101,4 @@ of the rank and nullity of T is the dimension of the domain of T.

- \ No newline at end of file + \ No newline at end of file diff --git a/source/linear-algebra/source/03-AT/samples/04.ptx b/source/linear-algebra/source/03-AT/samples/04.ptx index a28103b92..757a17342 100644 --- a/source/linear-algebra/source/03-AT/samples/04.ptx +++ b/source/linear-algebra/source/03-AT/samples/04.ptx @@ -1,6 +1,8 @@ -AT4 + + AT4 + <xref ref="AT4" text="global"/>

Let T: \IR^4 \rightarrow \IR^3 be the linear transformation given by the standard matrix \left[\begin{array}{cccc} 1 & 3 & 2 & -3 \\ 2 & 4 & 6 & -10 \\ 1 & 6 & -1 & 3 \end{array}\right]. @@ -35,4 +37,4 @@ Since there are only two pivots, the image (i.e. the span of the columns) is a 2

- \ No newline at end of file + \ No newline at end of file diff --git a/source/linear-algebra/source/03-AT/samples/05.ptx b/source/linear-algebra/source/03-AT/samples/05.ptx index f707511a9..83677bdfc 100644 --- a/source/linear-algebra/source/03-AT/samples/05.ptx +++ b/source/linear-algebra/source/03-AT/samples/05.ptx @@ -1,7 +1,9 @@ -AT5 + + AT5 + <xref ref="AT5" text="global"/>

Let V be the set of all pairs of numbers (x,y) of real numbers together with the following operations: @@ -128,4 +130,4 @@ Since these ordered pairs are different, the property fails to hold.

- \ No newline at end of file + \ No newline at end of file diff --git a/source/linear-algebra/source/03-AT/samples/06.ptx b/source/linear-algebra/source/03-AT/samples/06.ptx index c811f7788..770623103 100644 --- a/source/linear-algebra/source/03-AT/samples/06.ptx +++ b/source/linear-algebra/source/03-AT/samples/06.ptx @@ -1,5 +1,7 @@ -AT6 + + AT6 + <xref ref="AT6" text="global"/>

    @@ -76,4 +78,4 @@ The system has (infintely many) nontrivial solutions, so we that the set of poly is linearly dependent.

    - \ No newline at end of file + \ No newline at end of file diff --git a/source/linear-algebra/source/04-MX/samples/01.ptx b/source/linear-algebra/source/04-MX/samples/01.ptx index 6b7589946..a85b46cd9 100644 --- a/source/linear-algebra/source/04-MX/samples/01.ptx +++ b/source/linear-algebra/source/04-MX/samples/01.ptx @@ -1,6 +1,8 @@ -MX1 + + MX1 + <xref ref="MX1" text="global"/>

    Of the following three matrices, only two may be multiplied. @@ -95,4 +97,4 @@ ans =

    -     \ No newline at end of file + \ No newline at end of file diff --git a/source/linear-algebra/source/04-MX/samples/02.ptx b/source/linear-algebra/source/04-MX/samples/02.ptx index d215f06d7..b9eaee728 100644 --- a/source/linear-algebra/source/04-MX/samples/02.ptx +++ b/source/linear-algebra/source/04-MX/samples/02.ptx @@ -1,8 +1,9 @@ - - MX2 + + MX2 + <xref ref="MX2" text="global"/>

    Consider each of the following matrices.

    @@ -90,4 +91,4 @@ -     + diff --git a/source/linear-algebra/source/04-MX/samples/03.ptx b/source/linear-algebra/source/04-MX/samples/03.ptx index 86e5c2d52..4a49004ad 100644 --- a/source/linear-algebra/source/04-MX/samples/03.ptx +++ b/source/linear-algebra/source/04-MX/samples/03.ptx @@ -1,6 +1,8 @@ -MX3 + + MX3 + <xref ref="MX3" text="global"/>

    Let \mathcal{B}=\setList{\begin{bmatrix}-2\\-2\\1\end{bmatrix},\begin{bmatrix}-1\\-2\\-1\end{bmatrix},\begin{bmatrix}1\\3\\2\end{bmatrix}}, and \vec{v}=\begin{bmatrix}1\\2\\3\end{bmatrix}. @@ -47,4 +49,4 @@

    -     \ No newline at end of file + \ No newline at end of file diff --git a/source/linear-algebra/source/04-MX/samples/04.ptx b/source/linear-algebra/source/04-MX/samples/04.ptx index e3eb6e439..fe8497c3d 100644 --- a/source/linear-algebra/source/04-MX/samples/04.ptx +++ b/source/linear-algebra/source/04-MX/samples/04.ptx @@ -1,6 +1,7 @@ - - MX4 + + MX4 + <xref ref="MX4" text="global"/>

    Give a 3 \times 3 matrix C that may be used to perform the row operation -5 R_1 \to R_1.

    @@ -123,4 +124,4 @@ ans =     -     \ No newline at end of file + \ No newline at end of file diff --git a/source/linear-algebra/source/05-GT/samples/01.ptx b/source/linear-algebra/source/05-GT/samples/01.ptx index 2e143bc8f..1c30b17bc 100644 --- a/source/linear-algebra/source/05-GT/samples/01.ptx +++ b/source/linear-algebra/source/05-GT/samples/01.ptx @@ -1,6 +1,8 @@ -GT1 + + GT1 + <xref ref="GT1" text="global"/>

    Let A be any 4 \times 4 matrix with determinant @@ -93,4 +95,4 @@ so that M=RA. It follows that

    -     + \ No newline at end of file diff --git a/source/linear-algebra/source/05-GT/samples/02.ptx b/source/linear-algebra/source/05-GT/samples/02.ptx index fae2a3c25..485c7cede 100644 --- a/source/linear-algebra/source/05-GT/samples/02.ptx +++ b/source/linear-algebra/source/05-GT/samples/02.ptx @@ -1,7 +1,9 @@ -GT2 + + GT2 + <xref ref="GT2" text="global"/>

    Show how to compute the determinant of the matrix @@ -80,4 +82,4 @@ the determinant to a 3\times 3 matrix and then applying a formula: - \ No newline at end of file + \ No newline at end of file diff --git a/source/linear-algebra/source/05-GT/samples/03.ptx b/source/linear-algebra/source/05-GT/samples/03.ptx index 2677baf1e..03209d52f 100644 --- a/source/linear-algebra/source/05-GT/samples/03.ptx +++ b/source/linear-algebra/source/05-GT/samples/03.ptx @@ -1,7 +1,8 @@ - - GT3 + + GT3 + <xref ref="GT3" text="global"/> @@ -48,4 +49,4 @@

    -     \ No newline at end of file + \ No newline at end of file diff --git a/source/linear-algebra/source/05-GT/samples/04.ptx b/source/linear-algebra/source/05-GT/samples/04.ptx index 286a98ba9..e43692781 100644 --- a/source/linear-algebra/source/05-GT/samples/04.ptx +++ b/source/linear-algebra/source/05-GT/samples/04.ptx @@ -1,7 +1,9 @@ - GT4 + + GT4 + <xref ref="GT4" text="global"/>

    Explain how to find a basis for the eigenspace associated to the eigenvalue 3 in the matrix \left[\begin{array}{ccc} -7 & -8 & 2 \\ 8 & 9 & -1 \\ \frac{13}{2} & 5 & 2 \end{array}\right]. @@ -16,4 +18,4 @@ Thus we see the kernel is \setBuilder{\left[\begin{array}{c} -a \\ \frac{3}{ which has a basis of \left\{ \left[\begin{array}{c} -1 \\ \frac{3}{2} \\ 1 \end{array}\right] \right\}.

    -     \ No newline at end of file + \ No newline at end of file diff --git a/source/linear-algebra/source/meta/docinfo.ptx b/source/linear-algebra/source/meta/docinfo.ptx index 602dfc4d6..ab9983e36 100644 --- a/source/linear-algebra/source/meta/docinfo.ptx +++ b/source/linear-algebra/source/meta/docinfo.ptx @@ -9,7 +9,10 @@ \usepackage{tikz-cd} Learning Outcomes - + + + + diff --git a/source/linear-algebra/source/meta/sample-exercises.ptx b/source/linear-algebra/source/meta/sample-exercises.ptx index f04192791..bdc8540be 100644 --- a/source/linear-algebra/source/meta/sample-exercises.ptx +++ b/source/linear-algebra/source/meta/sample-exercises.ptx @@ -8,33 +8,48 @@ these solutions can give you an idea of the level of detail required for a complete solution.

    - - - - + + <xref ref="LE"/> + + + + + - - - - - - - + + <xref ref="EV"/> + + + + + + + + - - - - - - + + <xref ref="AT"/> + + + + + + + - - - - + + <xref ref="MX"/> + + + + + - - - - + + <xref ref="GT"/> + + + + + diff --git a/xsl/print.xsl b/xsl/print.xsl index dcb81dd70..97c1762ef 100644 --- a/xsl/print.xsl +++ b/xsl/print.xsl @@ -1,4 +1,8 @@ + + +]> @@ -190,4 +194,19 @@ + + + + + + % Renew tcolorbox for exercise + \tcbset{ divisionexercisestyle/.style={bwminimalstyle, runintitlestyle, exercisespacingstyle, before skip={3 ex}, breakable, before upper app={\setparstyle} } } + \renewtcolorbox{divisionexercise}[4] + {divisionexercisestyle, before title={}, title={\notblank{#2}{#2}{}}, after title={\notblank{#2}{\space}{}}, phantom={ + + \label{#4} + + \hypertarget{#4}{}}, after={\notblank{#3}{\par\rule{\workspacestrutwidth}{#3}\par\vfill}{\par}}} + + \ No newline at end of file From bb825218b4a0bf602b37d904102a56c3169d0d01 Mon Sep 17 00:00:00 2001 From: Drew Lewis <30658947+siwelwerd@users.noreply.github.com> Date: Fri, 8 May 2026 15:30:58 -0700 Subject: [PATCH 2/2] Apply suggestion from @siwelwerd --- xsl/print.xsl | 4 ---- 1 file changed, 4 deletions(-) diff --git a/xsl/print.xsl b/xsl/print.xsl index 97c1762ef..bd17861f7 100644 --- a/xsl/print.xsl +++ b/xsl/print.xsl @@ -1,8 +1,4 @@ - - -]>