Answer: In 1–6, (a) show that the given matrix A satisfies
Chapter 9, Problem 3E(choose chapter or problem)
In Problems 1–6, (a) show that the given matrix \(A\) satisfies \((A-r l)^{k}=0\) for some number \(r\) and some positive integer \(\mathrm{k} \text { and }(\mathrm{b})\) use this fact to determine the matrix \(e^{A t}\) [Hint: Compute the characteristic polynomial and use the Cayley–Hamilton theorem.]
\(A=\left[\begin{array}{ccc} { }^{2} & -1 & -1 \\ -3 & -1 & 1 \\ 9 & 3 & -4 \end{array}\right]\)
Equation Transcription:
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Text Transcription:
A
(A-rl)k=0
r
k and (b)
eAt
A=[ 2 1 -1 -3 -1 1 9 3 -4 ]
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