Mathematics · Bilinear and Quadratic Forms

A quadratic form Q(x, y, z) over &reals; represents 0 non-trivially if there exists (a, b, c) ∈ &reals; 3 \ {(0, 0, 0)} such that Q(a, b, c) = 0. Which of the following quadratic forms Q(x, y, z) over &reals; does NOT represent 0 non-trivially?

Verified Solution4 OptionsUpdated: October 2026👁️1 View

Correct answer

Q(x, y, z) = x 2 - xy + y 2 + z 2

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A quadratic form Q(x, y, z) over &reals; represents 0 non-trivially if there exists (a, b, c) &isin; &reals; 3 \ {(0, 0, 0)} such that Q(a, b, c) = 0. Which of the following quadratic forms Q(x, y, z) over &reals; does NOT represent 0 non-trivially?