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Chapter 5: Q6E (page 263)

TRUE OR FALSE?If matrices A and Sare orthogonal, then S-1ASis orthogonal as well.

Short Answer

Expert verified

The given statement is true.

Step by step solution

01

Properties of orthogonal matrices.

According to the properties of orthogonal matrices, the product of two orthogonal n脳nmatrices is also orthogonal and the inverse of ann脳nmatrix is also orthogonal.

02

Check whether the given statement is a true or false.

The given statement is if matrices A and S are orthogonal, then S-1ASmust is orthogonal as well.

It is given that A and S are orthogonal.

Here, S is orthogonal, so, S-1is also orthogonal.

This means, S-1ASis also orthogonal.

Then the given statement is true, by the properties of orthogonal matrices.

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Most popular questions from this chapter

Let Abe ann脳mmatrix. Is the formula(kerA)鈯�=im(AT)necessarily true? Explain.

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(a) Consider an matrix A such that A螕A=Im. It is necessarily true that? Explain.

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