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Chapter 8: Q47E (page 414)

47. If A=[1223], then there exist exactly four orthogonal2脳2matrices S such thatS-1ASis diagonal.

Short Answer

Expert verified

The given statement is FALSE.

Step by step solution

01

Check whether the given statement is TRUE or FALSE

Since is symmetric, it has an orthogonal basis consisting of eigenvectors. Let v藱1,v藱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=卤v藱1and Se2=卤v藱2OR Se1=卤v藱2and Se2=卤v藱1.

This gives a total of 8 possibilities for S.

02

Final Answer

Therefore, the given statement is FALSE.

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