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  1. \documentclass{article}
  2.  
  3. \usepackage[shortlabels]{enumitem}
  4. \usepackage[margin=0.75in]{geometry}
  5. \usepackage{amsmath,amsthm,amssymb}
  6. \usepackage{mathtools}
  7. \usepackage{etoolbox}
  8. \usepackage{tikz}
  9. \usepackage{collectbox}
  10.  
  11. \makeatletter
  12. \newcommand{\mybox}{%
  13.     \collectbox{%
  14.         \setlength{\fboxsep}{1pt}%
  15.         \fbox{\BOXCONTENT}%
  16.     }%
  17. }
  18. \makeatother
  19.  
  20. \usetikzlibrary{arrows,matrix,positioning}
  21.  
  22. \newcounter{alphasubsect}
  23. \def\alphainsubsection{0}
  24.  
  25. \let\oldsubsection=\subsection
  26. \def\subsection{%
  27.   \ifnum\alphainsubsection=1%
  28.     \addtocounter{alphasubsect}{1}
  29.   \fi%
  30. \oldsubsection}%
  31.  
  32. \renewcommand\thesubsection{%
  33.   \ifnum\alphainsubsection=1%
  34.     \Alph{alphasubsect}
  35.   \else%
  36.     \arabic{subsection}
  37.   \fi%
  38. }%
  39.  
  40. \newenvironment{alphasubsection}{%
  41.   \ifnum\alphainsubsection=1%
  42.     \errhelp={Let other blocks end at the beginning of the next block.}
  43.     \errmessage{Nested Alpha section not allowed}
  44.   \fi%
  45.   \setcounter{alphasubsect}{0}
  46.   \def\alphainsubsection{1}
  47. }{%
  48.   \setcounter{alphasubsect}{0}
  49.   \def\alphainsubsection{0}
  50. }%
  51.  
  52. \title{MATH150 PSet 1}
  53. \author{David}
  54. \date{\today}
  55.  
  56. \begin{document}
  57. \maketitle
  58.  
  59. \section*{Section 1.2}
  60.  
  61. \subsection*{Problem 4}
  62.  
  63. \[
  64. \begin{array}{r}
  65. (1) \\
  66. (2) \\
  67. (3) \\
  68. \end{array}
  69. \left[\begin{array}{cccc}
  70. 1 & 3 & 5 & 7 \\
  71. 3 & 5 & 7 & 9 \\
  72. 5 & 7 & 9 & 1 \\
  73. \end{array}\right] \thicksim
  74. \begin{array}{r}
  75. (1) \\
  76. (2) + -3(1) \\
  77. (3) + -5(1) \\
  78. \end{array}
  79. \left[\begin{array}{cccc}
  80. 1 & 3 & 5 & 7 \\
  81. 0 & -4 & -8 & -12 \\
  82. 0 & -8 & -16 & -34 \\
  83. \end{array}\right] \thicksim
  84. \begin{array}{r}
  85. (1) + 3/4(2)\\
  86. 1/4(2) \\
  87. (3) + -2(2) \\
  88. \end{array}
  89. \left[\begin{array}{cccc}
  90. 1 & 0 & -1 & -2 \\
  91. 0 & 1 & 2 & 3 \\
  92. 0 & 0 & 0 & -10 \\
  93. \end{array}\right] \thicksim
  94. \]
  95. \[
  96. \begin{array}{r}
  97. (1) - 1/5(3)\\
  98. (2) + 3/10(3) \\
  99. 1/10(3) \\
  100. \end{array}
  101. \left[\begin{array}{cccc}
  102. 1 & 0 & -1 & 0 \\
  103. 0 & 1 & 2 & 0 \\
  104. 0 & 0 & 0 & 1 \\
  105. \end{array}\right] \thicksim
  106. \]
  107. \mybox{
  108. \begin{tikzpicture}
  109.     \matrix [matrix of math nodes,left delimiter={[},right delimiter={]}] (m)
  110.     {
  111.         1 & 0 & -1 & 0 \\
  112.         0 & 1 & 2 & 0 \\
  113.         0 & 0 & 0 & 1 \\        
  114.     };  
  115.     \draw[color=red] (m-1-1.north west) -- (m-1-1.north east) -- (m-1-1.south east) -- (m-1-1.south west) -- (m-1-1.north west);
  116.     \draw[color=red] (m-2-2.north west) -- (m-2-2.north east) -- (m-2-2.south east) -- (m-2-2.south west) -- (m-2-2.north west);
  117.     \draw[color=red] (m-3-4.north west) -- (m-3-4.north east) -- (m-3-4.south east) -- (m-3-4.south west) -- (m-3-4.north west);
  118. \end{tikzpicture}
  119. \begin{tikzpicture}
  120.     \matrix [matrix of math nodes,left delimiter={},right delimiter={}] (m)
  121.     {
  122.         \mbox{} \\
  123.         \mbox{} \\
  124.         \& \\              
  125.         \mbox{} \\
  126.         \mbox{} \\
  127.     };
  128. \end{tikzpicture}
  129. \begin{tikzpicture}
  130.     \matrix [matrix of math nodes,left delimiter={[},right delimiter={]}] (m)
  131.     {
  132.         1 & 3 & 5 & 7 \\
  133.         3 & 5 & 7 & 9 \\
  134.         5 & 7 & 9 & 1 \\          
  135.     };  
  136.     \draw[color=red] (m-1-1.north west) -- (m-1-1.north east) -- (m-1-1.south east) -- (m-1-1.south west) -- (m-1-1.north west);
  137.     \draw[color=red] (m-2-2.north west) -- (m-2-2.north east) -- (m-2-2.south east) -- (m-2-2.south west) -- (m-2-2.north west);
  138.     \draw[color=red] (m-3-4.north west) -- (m-3-4.north east) -- (m-3-4.south east) -- (m-3-4.south west) -- (m-3-4.north west);
  139. \end{tikzpicture}
  140. }
  141.  
  142.  
  143. \end{document}
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