The quadratic form is negative for all values of and (other than ) if and only if:
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2 marksMathematicsMatrices, determinants and linear systemsDefiniteness and quadratic formsHardabout 2 min
UGC-NET 2024 Question 27: Matrices, determinants and linear systems
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The quadratic form ax² + by² + 2hxy is negative for all values of x and y (other than x=y=0) if and only if: (A) a>0 and |a h; h b|<0 (B) a<0 and |a h; h b|<0 (C) a<0 and |a h; h b|>0 (D) a<0 and |a h; h b|≠ 0
Also written as: The quadratic form ax^2 + by^2 + 2hxy is negative for all values of x and y (other than x=y=0) if and only if:
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What this question tests
This question is on Definiteness and quadratic forms, part of Matrices, determinants and linear systems in Mathematics.
Classifying symmetric matrices and quadratic forms as positive or negative definite.
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