If p (t) = c0 + c1t + c22 + + ct, define p (A)to be the

Chapter , Problem 5E

(choose chapter or problem)

Problem 5E

p (t) = c0 + c1t + c2 $t$ 2 + $\cdot{}\cdot{}\cdot{}$ + c $n$ t $n$ , define p (A)

to be the matrix formed by replacing each power of t in p (t) by the corresponding power of A (with A0 = I ). That is,

$p$ (A) = $c$ 0I + c1A + c2A2 + $\cdot{}\cdot{}\cdot{}$ + cnAn

Show that if $\lambda{}$ is an eigenvalue of A, then one eigenvalue of

p (A) is p ( $\lambda{})$ .

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