Explanation Given information: Assume the entries of all matrices are real numbers. Proof: Given: A Is an m x m symmetric matrix To prove: A 2 Is symmetric PROOF: Since A = ( a i j ) is an m × m symmetric matrix: a i j = a j i for all i , j = 1 , 2 , ... , m Let us then determine if the element of A 2 = ( b i j ) also symmetric property ( b i j = b j i ) . b i j = i j th entry of A 2 = i j th entry of A ⋅ A = ∑ r = 1 n a i r a r j = ∑ r = 1 n

5th Edition

ISBN: 9781337694193

Author: EPP, Susanna S.

Publisher: Cengage Learning,

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Matrices

‘Matrices’ is the plural form of the word matrix, and it is basically a spreadsheet in the form of a box. In mathematics, various functions can be carried out with matrices. Generally, a matrix comes in the shape of a square or rectangle. The elements ar…

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Chapter 10.2, Problem 15ES

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

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