diff --git a/publication/publication-619.ptx b/publication/publication-619.ptx index 76f1f697c..e7b4340e5 100644 --- a/publication/publication-619.ptx +++ b/publication/publication-619.ptx @@ -67,6 +67,10 @@ papersize={7in,10in},margin=1in + + + + diff --git a/source/linear-algebra/source/01-LE/01.ptx b/source/linear-algebra/source/01-LE/01.ptx index 9b0099eed..cdd87d1ba 100644 --- a/source/linear-algebra/source/01-LE/01.ptx +++ b/source/linear-algebra/source/01-LE/01.ptx @@ -993,7 +993,7 @@ Augmented matrix: - + Individual Practice diff --git a/source/linear-algebra/source/01-LE/02.ptx b/source/linear-algebra/source/01-LE/02.ptx index d7f1873ca..4f22d4344 100644 --- a/source/linear-algebra/source/01-LE/02.ptx +++ b/source/linear-algebra/source/01-LE/02.ptx @@ -540,7 +540,7 @@ most complicated to simplest (in your opinion). - +

Here we've written the sorted linear systems from @@ -815,7 +815,7 @@ This will keep you from undoing your progress towards an RREF matrix.

- +

Complete the following RREF calculation (multiple row operations may be needed diff --git a/source/linear-algebra/source/02-EV/01.ptx b/source/linear-algebra/source/02-EV/01.ptx index 2558410ca..38958d0cb 100644 --- a/source/linear-algebra/source/02-EV/01.ptx +++ b/source/linear-algebra/source/02-EV/01.ptx @@ -116,7 +116,7 @@ we refer to this real number as a scalar. - +

Consider \vspan\left\{\left[\begin{array}{c}1\\2\end{array}\right]\right\}. @@ -165,7 +165,7 @@ we refer to this real number as a scalar. - +

Consider \vspan\left\{\left[\begin{array}{c}1\\2\end{array}\right], @@ -251,7 +251,7 @@ we refer to this real number as a scalar. - +

Sketch a representation of all the vectors belonging to diff --git a/source/linear-algebra/source/02-EV/03.ptx b/source/linear-algebra/source/02-EV/03.ptx index 216e5a359..1d03c73b4 100644 --- a/source/linear-algebra/source/02-EV/03.ptx +++ b/source/linear-algebra/source/02-EV/03.ptx @@ -132,7 +132,7 @@ - +

Consider an arbitrary homogeneous vector equation x_1 \vec{v}_1 + \cdots+x_n \vec{v}_n = \vec{0}. @@ -495,6 +495,8 @@ Proofs of an equality \mathrm{LEFT}=\mathrm{RIGHT} should generally be of

  • Using two chains of equalities: +

    +

    \mathrm{LEFT} &= \cdots & \mathrm{RIGHT} &=\cdots diff --git a/source/linear-algebra/source/02-EV/06.ptx b/source/linear-algebra/source/02-EV/06.ptx index e6c563daa..3e32d48e4 100644 --- a/source/linear-algebra/source/02-EV/06.ptx +++ b/source/linear-algebra/source/02-EV/06.ptx @@ -207,7 +207,7 @@ T=\left\{ - +

    Even though we found different bases for them, \vspan S and \vspan T are exactly the same subspace of \IR^4, diff --git a/source/linear-algebra/source/03-AT/02.ptx b/source/linear-algebra/source/03-AT/02.ptx index 72fc78efc..797d87976 100644 --- a/source/linear-algebra/source/03-AT/02.ptx +++ b/source/linear-algebra/source/03-AT/02.ptx @@ -704,7 +704,7 @@ T\left(\left[\begin{array}{c} -5 \\ 0 \\ -3 \\ -2 \end{array}\right]\right) - + Exercises

    Exercises available at diff --git a/source/linear-algebra/source/03-AT/03.ptx b/source/linear-algebra/source/03-AT/03.ptx index c9ff00589..1e7430d39 100644 --- a/source/linear-algebra/source/03-AT/03.ptx +++ b/source/linear-algebra/source/03-AT/03.ptx @@ -235,7 +235,7 @@ Let T: \IR^3 \rightarrow \IR^2 be the linear transformation with the foll - +

    Let T: \IR^4 \rightarrow \IR^3 be the linear transformation whose standard matrix is: diff --git a/source/linear-algebra/source/03-AT/04.ptx b/source/linear-algebra/source/03-AT/04.ptx index 61284e73c..92ffcfb5d 100644 --- a/source/linear-algebra/source/03-AT/04.ptx +++ b/source/linear-algebra/source/03-AT/04.ptx @@ -686,7 +686,7 @@ means T is (A) injective, (B) surjective, or

    - +

    What can you conclude about the linear map diff --git a/source/linear-algebra/source/05-GT/01.ptx b/source/linear-algebra/source/05-GT/01.ptx index cb62fec92..45f6164ac 100644 --- a/source/linear-algebra/source/05-GT/01.ptx +++ b/source/linear-algebra/source/05-GT/01.ptx @@ -67,7 +67,7 @@ standard matrix A = \left[\begin{array}{cc} 2 & 0 \\ 0 & 3 \end{array transforms the unit square.

    - + \begin{tikzpicture} \fill[red!50!white] (0,0) rectangle (1,1); @@ -1073,7 +1073,7 @@ Or we may use a formula: - + Individual Practice diff --git a/source/linear-algebra/source/05-GT/04.ptx b/source/linear-algebra/source/05-GT/04.ptx index a56b03c2b..e41cc478a 100644 --- a/source/linear-algebra/source/05-GT/04.ptx +++ b/source/linear-algebra/source/05-GT/04.ptx @@ -120,7 +120,7 @@ associated with the eigenvalue 2. - + Individual Practice diff --git a/source/linear-algebra/source/applications/pagerank.ptx b/source/linear-algebra/source/applications/pagerank.ptx index 05f007c96..c9a05f34e 100644 --- a/source/linear-algebra/source/applications/pagerank.ptx +++ b/source/linear-algebra/source/applications/pagerank.ptx @@ -168,7 +168,7 @@ This corresponds to the page rank system:
    - + \begin{tikzpicture} \begin{scope}[every node/.style={circle,thick,draw}] @@ -260,7 +260,7 @@ That is, find the eigenspace associated with \lambda=1 for the matrix

    - + \begin{tikzpicture} \begin{scope}[every node/.style={circle,thick,draw}] diff --git a/xsl/print.xsl b/xsl/print.xsl index bd17861f7..039bc72b6 100644 --- a/xsl/print.xsl +++ b/xsl/print.xsl @@ -203,6 +203,10 @@ \label{#4} \hypertarget{#4}{}}, after={\notblank{#3}{\par\rule{\workspacestrutwidth}{#3}\par\vfill}{\par}}} + + + + \setlength\extrarowheight{5pt} \newcommand{\sectionbreak}{\clearpage\thispagestyle{plain}} \ No newline at end of file