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Chapter 8: Q43E (page 414)

43. If Ais indefinite, then 0 must be an eigenvalue of A.

Short Answer

Expert verified

The given statement is FALSE.

Step by step solution

01

Check whether the given statement is TRUE or FALSE

Recall that the matrix is indefinite if the Eigenvalues are both positive and negative.

Let us take an example to check whether the given statement is true or not.

A=100-1

Then, the corresponding quadratic form is q(x)=x12-x22.

q( 1,1 ) = 0 which implies that q (x) is indefinite.

Thus, A is indefinite but 0 is not an eigenvalue of A.

02

Final Answer

The given statement is FALSE.

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