Finding a Power of a Matrix In Exercises 33-36, use the result of Exercise 31 to find the power of A shown. A = [ 1 3 2 0 ] , A 7 Proof Let A be a diagonalizable n × n matrix and let P be an invertible n × n matrix such that B = P − 1 A P is the diagonal form of A . Prove that A k = P B k P − 1 , where k is a positive integer.
Finding a Power of a Matrix In Exercises 33-36, use the result of Exercise 31 to find the power of A shown. A = [ 1 3 2 0 ] , A 7 Proof Let A be a diagonalizable n × n matrix and let P be an invertible n × n matrix such that B = P − 1 A P is the diagonal form of A . Prove that A k = P B k P − 1 , where k is a positive integer.
Solution Summary: The author explains how to find the matrix A7 for the given matrix: A=left[cc1& 3 2& 0
Finding a Power of a Matrix In Exercises 33-36, use the result of Exercise 31 to find the powerof A shown.
A
=
[
1
3
2
0
]
,
A
7
Proof Let A be a diagonalizable
n
×
n
matrix and let P be an invertible
n
×
n
matrix such that
B
=
P
−
1
A
P
is the diagonal form of A. Prove that
A
k
=
P
B
k
P
−
1
, where k is a positive integer.
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