\documentclass[11pt]{article}
\usepackage{jeffe,handout,multicol,tikz,kgm}
\usepackage[top=0.56in]{geometry}

\newcommand{\kgmcomment}[1]{}

\newcommand{\pd}[2]{\frac{\partial #1}{\partial #2}}

\begin{document}


%\makeatletter
%\def\@oddfoot{\hfill \tikz \node[draw] {over} ; }
%\makeatother

\makeatletter
\def\@oddfoot{}
\makeatother

\newcommand{\dd}{\partial}
\newcommand{\mtrix}[2]{%
	\left[%
	\begin{array}{*{#1}{r}}
		#2
	\end{array}
	\right]%
}

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~
\vspace{2cm}

\noindent
\textbf{Directions:}  
\begin{enumerate}
	\item Write your name with one character in each box below.
	\item Show all work.  No credit for answers without work.
\end{enumerate}

\newpage
\headers{Math251}{Quiz 1}{Aug 29, 2025}

~
\vspace{1.5cm}

\begin{enumerate}

\newcommand{\myspc}{\vspace{2cm}\\~}
\item\ppoints{4}{1} Compute the following matrices if defined.
\begin{align*}
	A &= \mtrix{2}{1 & -1 \\ 2 & 4}  &  B &= \mtrix{2}{ 2 & 0 \\ 0 & 3 \\ 1 & -3 }  & C &= \mtrix{2}{3 & -2 \\ 1 & 5}  & D &= \mtrix{3}{-1 & 2 & 5}
\end{align*}
\begin{multicols}{2}
\begin{enumerate}
	\item $A + 2C$
	\myspc
	\item $BC$
	\myspc
	
	\columnbreak
	\item $DD^T$
	\myspc
	\item $D^TD$
	\myspc
\end{enumerate}
\end{multicols}

\item\points{6} Solve the following system.
\[  \begin{array}{*{7}{r}}
   -3x_1  &+&   4x_2   &-&  4x_3  &=&  1\\
  -11x_1  &+&  16x_2   &-& 15x_3  &=&  2\\
	-x_1  &+&    x_2   &-&   x_3  &=&  3
    \end{array}
\]
\vfill

\end{enumerate}
\end{document}
