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\textbf{Math 228: Intro to Lin Alg \& Diff Eqns}
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\textbf{Quiz 1}\quad \textsl{Jan. 24, 2002}
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1. Determine whether the linear system represented by each of the
following augmented matrices has no solution, exactly one solution,
or infinitely many solutions.

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a) $\left[\begin{array}{cccc}
1&1&1&1\\
0&0&1&2\\
0&0&0&1\end{array}\right]$

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b) $\left[\begin{array}{cccc}
1&1&1&1\\
1&2&3&4\\
2&3&4&5\end{array}\right]$

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c) $\left[\begin{array}{cccc}
1&1&1&1\\
0&1&2&3\\
0&0&1&2\end{array}\right]$

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2. Let $A = \left[\begin{array}{cc}0&1\\1&0\end{array}\right]$,
$B = \left[\begin{array}{cc}1&2\\3&4\end{array}\right]$, and
$C = \left[\begin{array}{ccc}1&-1&2\\-1&2&1\end{array}\right]$.
Carry out each of the following matrix operations, if it is defined.

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a) $2A - B$

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b) $C\cdot A$

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c) $B\cdot C$

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