   Chapter 10.2, Problem 17ES ### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193

#### Solutions

Chapter
Section ### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193
Textbook Problem
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# In 14-18, assume the entries of all matrices are real numbers.Use mathematical induction and the result of exercise 16 to prove that if A is any m × m matrix, then A”A=A”A for each integer n ≥ 1 .

To determine

To determine: IfA Is any m×m matrix, then AnA=AAn for all integers n1.

Explanation

Given information: A Is any m×m matrix, then AnA=AAn for all integers n1.

Assume the entries of all matrices are real numbers.

Proof:

Given: A Is an m×m matrix

To proof: AnA=AAn for all integers n1

PROOF:

Let P(n) be "AnA=AAn"

Basis step n = 1

AnA = A1A = AA = AA1 = AAnThus P(1) is true.

Inductive step:

Let P(k) be true, thus AkA = AAk

We need to prove that P ( k + 1) is true

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