16.-Linear-Algebra-by-Kenneth-Hoffman · Problem 10.2.3

Bilinear Forms

Mathematics — Linear Algebra · non-degenerate-quadratic-form

Problem

Let q(x1,x2)=ax12+bx1x2+cx22q(x_1, x_2) = ax_1^2 + bx_1 x_2 + cx_2^2 be the quadratic form associated with a symmetric bilinear form ff on R2R^2. Show that ff is non-degenerate if and only if b2−4ac≠0b^2 - 4ac \neq 0.

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