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Problem 5 Let a matrix A be given by 2 -23 1 3 -1 (i) Find the characteristic polynomial of A: p(s) = det(-A). Express (s-A)-

Let a matrix A be given by

A =

$egin{bmatrix} 2 &-2 &3 \ 1&1 &1 \ 1&3 &-1 end{bmatrix}$

(i) Find the characteristic polynomial of A: p(s) = det(SI - A). Express (SI - A)^-1 in the form
(SI - A)^-1 = N(s)/p(s)

using the recursive formulas for computing N(s).
(ii) Find $e^{At}$ using the result in (i).

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