Solution: In 17–20 the given vectors are solutions of a
Chapter 8, Problem 17E(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 \((-\infty, \infty)\).
\(\mathbf{X}_{1}=\left(\begin{array}{l}
1 \\
1
\end{array}\right) e^{-2 t}
\), \(\mathbf{X}_{2}=\left(\begin{array}{r}
1 \\
-1
\end{array}\right) e^{-6 t}
\)
Text Transcription:
mathbf X^prime=mathbf A mathbf X
(-infty, infty)
mathbf X_1=({array} l 1 1 {array}) e^-2 t
mathbf X_2=({array} r 1 -1 {array}) e^-6 t
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