Question

(a)

For the following quadratic forms gi(x) write down the associated symmetric matrix Ai such that gi(x) = xT Aix.

g1(x1, x2) = x21 − 2x1x2 + 4x2

g2(x1, x2) = 4x21 − 6x1x2 + x2

g3(x1, x2, x3) = 3x21 + 3x2 + 5x23 + 2x1x2 − 2x1x3 − 2x2x3

g4(x1, x2, x3) = −3x21 − x2 + 8x2x3 − 16x23

(b) Determine the definiteness of g1(x) and g3(x) using the method of eigenvalues.

(c) Determine the definiteness of g2(x) and g4(x) using the method of minors.

Answer 1