In 1–6, (a) show that the given matrix A

Chapter 9, Problem 6E

(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.]    

                     

\(A=\left[\begin{array}{rrr}  0 & 1 & 0 \\  0 & 0 & 1 \\  -1 & -3 & -3  \end{array}\right]\)

Equation Transcription:

[ ]  

Text Transcription:

A

(A-rl)^k=0

r

k and (b)

e^At

A=[  0           1         0   -1   0           0         1   -3    -3         ]  

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