Consider the following quadratic forms q(x1, x2) = 3x1^2 − 6x1x2 + 11x2^2 and r(x1, x2,...

Consider the following quadratic forms

q(x1, x2) = 3x1^2 − 6x1x2 + 11x2^2 and

r(x1, x2, x3) = x1^2 − x2^2+x3^2+ 2x1x2 − 6x1x3+2x2x3,

on R 2 and R 3 , respectively. In both cases do the following.

(a) Find the symmetric matrix A representing the quadratic form.

(b) Find a corresponding orthogonal matrix P of eigenvectors of that matrix.

(c) Write down the maximum and minimum values of the quadratic form over the unit vectors (in R 2 and R 3 , respectively).

Please include steps and answer a), b) and c)

Solutions

Expert Solution

Colby Messinger answered 1 year ago

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