In 1–6, (a) show that the given matrix A
Chapter 9, Problem 5E(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.]
\(A=\left[\begin{array}{rrr} -2 & 0 & 0 \\ 4 & -2 & 0 \\ 1 & 0 & -2 \end{array}\right]\)
Equation Transcription:
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Text Transcription:
A
(A-rl)^k=0
r
k and (b)
e^At
A=[ -2 0 0 4 -2 0 1 0 -2 ]
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