Solved: In 17–20 the given vectors are solutions of a
Chapter 8, Problem 20E(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 \((-\infty, \infty)\).
\(\mathbf{X}_{1}=\left(\begin{array}{r}
1 \\
6 \\
-13
\end{array}\right)
\), \(\mathbf{X}_{2}=\left(\begin{array}{r}
1 \\
-2 \\
-1
\end{array}\right) e^{-4 t}
\), \(\mathbf{X}_{3}=\left(\begin{array}{r}
2 \\
3 \\
-2
\end{array}\right) e^{3 t}
\)
Text Transcription:
mathbf X^prime=mathbf A mathbf X
(-infty, infty)
mathbf X_1=({array} r 1 6 -13 {array})
mathbf X_2=({array} r 1 -2 -1 {array}) e^-4 t
mathbf X_3=({array} r 2 3 -2 {array}) e^3 t
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