The Characteristic Polynomial of a 5 × 5 Matrix Is$$\text { Find a formula for } A ^ { k } \text {, given that } A = P D P - 1 \text {, where } P \text { and } D \text { are given below. }$$

Question

Examlex · Accepted Answer

The Answer is To find the eigenvalues and their multiplicities, we first need to factor the characteristic polynomial of the 5 × 5 matrix. Once we have the factors, we can determine the eigenvalues and their multiplicities.

As for the formula for

A^k

, given that

A = PDP^{-1}

, where

P

and

D

are given below, we can use the formula

A^k = PD^kP^{-1}

to find the kth power of

A

. This formula allows us to easily compute higher powers of

A

using the diagonal matrix

D

and the invertible matrix

P

.

The Characteristic Polynomial of a 5 × 5 Matrix Is $\text { Find a formula for } A ^ { k } \text {, given that } A = P D P - 1 \text {, where } P \text { and } D \text { are given below. }$

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