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Chapter 3: Q5P (page 141)

Show that the product AA韦is a symmetric matrix.

Short Answer

Expert verified

It is shown that AA韦is a symmetric matrix.

Step by step solution

01

Given information

The given product is AA韦, where Aand A韦 are two matrices.

02

Definition of a symmetric matrix

A matrix Ais said to be symmetric if A=A韦, where T represents transpose of a matrix.

03

To show that   is a symmetric matrix

To prove the product AA韦is a symmetric matrix, it is necessary to show that (AAT)=AATT.

It is known that, ABT=BTAT. Therefore, AAT=AATTcan be written as follows:

AATT=ATTAT=AAT鈭�ATT=A

Thus, AAT=AATT

Hence, the product AAT is a symmetric matrix.

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