Log In Start studying!

Select your language

Suggested languages for you:
Answers without the blur. Sign up and see all textbooks for free! Illustration


Linear Algebra With Applications
Found in: Page 414
Linear Algebra With Applications

Linear Algebra With Applications

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

Answers without the blur.

Just sign up for free and you're in.


Short Answer

47. If A=[1223], then there exist exactly four orthogonal 2×2matrices S such that S-1AS is diagonal.

The given statement is FALSE.

See the step by step solution

Step by Step Solution

Step 1: Check whether the given statement is TRUE or FALSE

Since is symmetric, it has an orthogonal basis consisting of eigenvectors. Let v˙1,v˙2be unit orthogonal eigenvectors of A. Since S is orthogonal diagonal zing matrix of A,S must map e1,e2to orthogonal eigenvectors.

Thus, we have either Se1=±v˙1and Se2=±v˙2OR Se1=±v˙2 and Se2=±v˙1.

This gives a total of 8 possibilities for S.

Step 2: Final Answer

Therefore, the given statement is FALSE.

Recommended explanations on Math Textbooks

94% of StudySmarter users get better grades.

Sign up for free
94% of StudySmarter users get better grades.