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Chapter 5: Q14E (page 233)

If the nxn matrices Aand Bare symmetric and Bis invertible, which of the matrices in Exercise 13 through 20 must be symmetric as well? -B.

Short Answer

Expert verified

The Matrix -B is symmetric.

Step by step solution

01

Definition of symmetric matrix.

A square matrix is symmetric matrix ifA=A-T

02

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,kA=kAT it gives,

-BT=-BT=-B

Therefore, -B is a symmetric matrix.

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Find the least squarex鈬赌* of the systemAx鈬赌=b whereA=[123456789] andb鈬赌=[100] .

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20.[235046007]

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