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Chapter 5: Q10E (page 263)

If is a symmetric matrix, then must be symmetric as well.

Short Answer

Expert verified

The given statement is true.

Step by step solution

01

Definition of a symmetric matrix.

Suppose A is amatrix.

Then the matrix is said to be symmetric matrix, ifAT=A.

02

Check whether the given statement is a true or false.

The given statement A is if is a symmetric matrix, the *7A must be symmetric as well.

It is given that A is symmetric matrix.

This means,AT=A

Here, the matrix 7Ais symmetric, if role="math" localid="1659503234480" 7AT=7A.

Check:

7AT=7A=7A

So,7AT=7A .

This means, 7A is also a symmetric matrix.

Then the given statement is true.

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Using paper and pencil, perform the Gram-Schmidt process on the sequences of vectors given in exercises 1 through 14.

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