Let A be a diagonalizable n x n matrix and let P be an invertible n x n matrix such that B = P-'AP is the diagonal form of A. Prove that Ak = PBKP-1, where k is a positive integer. Use the result above to find the indicated power of A. -10 -18 A5 A = 11 A5 =

Let A be a diagonalizable n x n matrix and let P be an invertible n x n matrix such that B = P-'AP is the diagonal form of A. Prove that Ak = PBKP-1, where k is a positive integer. Use the result above to find the indicated power of A. -10 -18 A5 A = 11 A5 =

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter2: Matrices

Section2.3: The Inverse Of A Matrix

Problem 79E: Let A,D, and P be nn matrices satisfying AP=PD. Assume that P is nonsingular and solve this for A....

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Question

(Linear Algebra)

10.

7.2

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Let A be a diagonalizable n × n matrix and let P be an invertible n × n matrix such that B =
P-'AP is the diagonal form of A. Prove that AK = PBKP-1, where k is a positive integer.
Use the result above to find the indicated power of A.
-10 -18
A =
45
6.
11
A5 =
II

Branch of mathematics concerned with mathematical structures that are closed under operations like addition and scalar multiplication. It is the study of linear combinations, vector spaces, lines and planes, and some mappings that are used to perform linear transformations. Linear algebra also includes vectors, matrices, and linear functions. It has many applications from mathematical physics to modern algebra and coding theory.

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