Answer: In 17–20 the given vectors are solutions of a
Chapter 8, Problem 19E(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 \((-\infty, \infty)\).
\(\mathbf{X}_{1}=\left(\begin{array}{r}
1 \\
-2 \\
4
\end{array}\right)+t\left(\begin{array}{l}
1 \\
2 \\
2
\end{array}\right)
\), \(\mathbf{X}_{2}=\left(\begin{array}{r}
1 \\
-2 \\
4
\end{array}\right)
\), \(\mathbf{X}_{3}=\left(\begin{array}{r}
3 \\
-6 \\
12
\end{array}\right)+t\left(\begin{array}{l}
2 \\
4 \\
4
\end{array}\right)
\)
Text Transcription:
mathbf X^prime=mathbf A mathbf X
(-infty, infty)
mathbf X_1=({array} r 1 -2 4 {array})+t ({array} l 1 2 2 {array})
mathbf X_2=({array} r 1 -2 4 {array})
mathbf X_3=({array} r 3 -6 12 {array})+t ({array} l 2 4 4 {array})
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