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Linear Algebra With Applications
Found in: Page 233
Linear Algebra With Applications

Linear Algebra With Applications

Book edition 5th
Author(s) Otto Bretscher
Pages 442 pages
ISBN 9780321796974

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Short Answer

Question: If the n×n matrices A and B are symmetric and B is invertible, which of the matrices in Exercise 13 through 20 must be symmetric as well?A+B.

The Matrix A + B is symmetric.

See the step by step solution

Step by Step Solution

Step 1: Definition of symmetric matrix.

A square matrix is symmetric matrix if A=AT

Step 2: Verification whether the given matrix is symmetric.

Given that A and B are symmetric matrices and B is invertible.

Since A is symmetric, then A=AT.

Then by properties of transpose, A+BT=AT+BT =A+B it gives,

Therefore, A + B is a symmetric matrix.

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