Question: Show how to classify a quadratic form Q(x) = x T Ax, when and det A 0, without finding the eigenvalues of A. Verify

Show how to classify a quadratic form Q(x) = x^TAx, when A = || a b b d and det A ≠ 0, without finding the eigenvalues of A.

Verify the following statements:

a. Qis positive definite if det A > 0 and a > 0.

b. Q is negative definite if det A > 0 and a

c. Q is indefinite if det A

A = || a b b d

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ANSWER To classify a quadratic form Qx xTAx without finding the eigenvalues of A we can analyze the signs of the elements of A and the determinant of ... View full answer

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