Page 560 - Elementary_Linear_Algebra_with_Applications_Anton__9_edition

EXAMPLE 6 Power of a Matrix
Use 10 to find , where

Solution

We showed in Example 1 that the matrix A is diagonalized by

and that

Thus, from 10,

(11)

Remark With the method in the preceding example, most of the work is in diagonalizing A. Once that work is done, it can be

used to compute any power of A. Thus, to compute we need only change the exponents from 13 to 1000 in 11.

Exercise Set 7.2

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Let A be a matrix with characteristic equation . What are the possible dimensions for eigenspaces
1. of A?

Let
2.