7. (10 points) Let Q : R² → R be the quadratic form defined by Q(x) = 6x7 – 12:x1#2 + x3. (a) Write down the symmetric matrix associated with Q. (b) Classify Q as positive definite, negative definite,...

Extracted text: 7. (10 points) Let Q : R² → R be the quadratic form defined by Q(x) = 6x7 – 12:x1#2 + x3. (a) Write down the symmetric matrix associated with Q. (b) Classify Q as positive definite, negative definite, or indefinite. Find the maximum and minimum values of Q(x) subject to the constraint a? +x} = 1. (You (c) must use linear algebra for this part; no credit for using other methods, such as Lagrange multipliers from multivariable calculus.)