need help on these two Linear Algebra question.
Thank you very much.
4. Let Q be the quadratic form
Q(x) = 5x2 - y2 + 2z2 + 2xy + 10xz - 4yz
on ℝ3. Find a symmetric matrix A such that Q(x) = xTAx.
This quadratic form is indenite. Demonstrate this using the values Q(x1) and Q(x2),
for suitably chosen vectors x1 and x2.
5. For the below quadratic form:
Q(x1; x2; x3) = 2(x12+ x22+ x32 - x1x2 + x1x3 - x2x3)
a) Find the symmetric matrix A such that Q(X) = XTAX.
b) Find an orthogonal matrix P such that the change of variables y = PTx transforms
Q into a quadratic form Q′(y) with no cross product term. Write down the new
quadratic form Q′(y).
c) Classify Q as positive/negative denite or indenite. Justify the answer.
4) A = ⎝ ⎛ 5 1 5 1 − 1 − 2 5 − 2 2 ... View the full answer