   Chapter 10.2, Problem 15ES ### 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.Prove that if A is the m × m symmetric matrix, then A2is symmetric.

To determine

Prove that if A Is an m × m symmetric matrix, then A2 Is symmetric.

Explanation

Given information:

Assume the entries of all matrices are real numbers.

Proof:

Given: A Is an m x m symmetric matrix

To prove: A2 Is symmetric

PROOF:

Since A=(a ij) is an m×m symmetric matrix: aij=aji for all i,j=1,2,...,mLet us then determine if the element of A2=(b ij) also symmetric property (b ij=b ji).

bij=ijth entry of A2    =ijth entry of AA    =r=1na ira rj    =r=1n

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