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\author{Teschl Gerald}
\title{Quiz 2}
\date{11 Sep. 1995}

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\hfill {\bf Name}: $\ul{\hspace*{5cm}}$\\[2mm]
\hspace*{2mm}\hfill {\bf ID \#}: $\ul{\hspace*{5cm}}$\\[5mm]

{\Huge Quiz 2}\\[8mm]

\noindent 1) Let
\bd
A = \left[ \ba{cc} 1 & 3 \\ 1 & 4\ea\right].
\ed
What do you need to choose for $x$ such that
\bd
A^{-1} = \left[ \ba{cc} x & -3 \\ -1 & 1\ea\right] ?
\ed

a) $x=1$ b) $x=2$  c) $x=3$ d) $x=4$ e) $A$ is not invertible \hfill (4pts)\\[8mm]

\noindent 2) What is the dimension of the following product
\bd
\left[ \ba{c} 1 \\ 2 \ea\right] \left[ \ba{ccc} 1 & 2 & 3\\ 4 & 5 & 6\ea\right] \left[ \ba{c} 1 \\ 2 \\ 3\ea\right] ?
\ed

a) 2 rows, 1 column b) 2 rows, 3 columns  c)  1 row, 3 columns\\ d) 2 rows, 3 columns e) product is not defined \hfill(3pts)\\[8mm]

\noindent 3) Consider the system
\beas
x+y &=& 0\\ z+y &=& 1 \\ x &=& z.
\eeas
What is the corresponding augmented matrix?
\bd
\mb{a)} \left[ \ba{cc} 1 & 1 \\ 1 & 1 \\ 0 & 1 \ea\right| \left. \ba{c} 0 \\ 1 \\ 1\ea\right] \quad
\mb{b)} \left[ \ba{ccc} 1 & 1 & 0 \\ 0 & 1 & 1 \\ 1 & 0 & 0 \ea\right| \left. \ba{c} 0 \\ 1 \\ 1\ea\right] \quad 
\mb{b)} \left[ \ba{cc} 1 & 1 \\ 1 & 1 \\ 1 & - 1\ea\right| \left. \ba{c} 0 \\ 1 \\ 0\ea\right]
\ed
\bd
\mb{d)} \left[ \ba{ccc} 1 & 1 & 0 \\ 0 & 1 & 1 \\ 1 & 0 & -1\ea\right| \left. \ba{c} 0 \\ 1 \\ 0\ea\right] \quad 
\mb{e)} \left[ \ba{ccc} 1 & 1 & 0 \\ 1 & 1 & 0 \\ 1 & 0 & -1\ea\right| \left. \ba{c} 0 \\ 1 \\ 0\ea\right] 
\ed
\vspace*{3mm}\hfill (3pts)\\[8mm]


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