In 17–20 the given vectors are solutions of a system
Chapter 8, Problem 18E(choose chapter or problem)
In Problems 17–20 the given vectors are solutions of a system \(\mathbf{X}^{\prime}=\mathbf{A} \mathbf{X}\). Determine whether the vectors form a fundamental set on the interval \((-\infty, \infty)\).
\(\mathbf{X}_{1}=\left(\begin{array}{r}
1 \\
-1
\end{array}\right) e^{t}
\), \(\mathbf{X}_{2}=\left(\begin{array}{l}
2 \\
6
\end{array}\right) e^{t}+\left(\begin{array}{r}
8 \\
-8
\end{array}\right) t e^{t}
\)
Text Transcription:
mathbf X^prime=mathbf A mathbf X
(-infty, infty)
mathbf X_1=({array} r1 -1 {array}) e^t
mathbf X_2=({array} l 2 6 {array}) e^t+ ({array} r 8 -8 {array}) t e^t
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