16.-Linear-Algebra-by-Kenneth-Hoffman · Problem 10.2.1

Bilinear Forms

Mathematics — Linear Algebra · quadratic-forms-symmetric-bilinear

Problem

The following expressions define quadratic forms

q

R^2

. Find the symmetric bilinear form

f

corresponding to each

q

. (a)

ax_1^2

. (b)

bx_1 x_2

. (c)

cx_2^2

. (d)

2x_1^2 - \frac{1}{3}x_1 x_2

. (e)

x_1^2 + 9x_2^2

. (f)

3x_1 x_2 - x_2^2

. (g)

4x_1^2 + 6x_1 x_2 - 3x_2^2