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\textbf{Math 325: Differential Equations}
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\textbf{Quiz 3}\quad \textsl{Oct. 15, 1997}

\begin{enumerate}

\problemspace
\item
(4 pts.) Determine whether the following vector functions are linearly
independent. (Justify your answer.)
\[
\X_1 = \left[\begin{array}{c}1  \\ t  \\ t^2\end{array}\right],\quad
\X_2 = \left[\begin{array}{c}t  \\ t^2\\ t^3\end{array}\right],\quad
\X_3 = \left[\begin{array}{c}t^2\\ t^3\\ t^4\end{array}\right]
\]

\answerspace

\problemspace
\item
(6 pts.) Find the eigenvalues and corresponding eigenvectors of the following
matrix.
\[
\left[ \begin{array}{ccc}
0 & 6 & 0\\
3 & 0 & 3\\
0 &-3 & 0
\end{array} \right]
\]
\answerspace

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