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need help on these two Linear Algebra question.

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4. Let Q be the quadratic form

Q(x) = 5x2 - y2 + 2z2 + 2xy + 10xz - 4yz

on 3. 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.

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4)   A = ​ ⎝ ​ ⎛ ​ ​ ​ 5 ​ 1 ​ 5 ​ ​ ​ 1 ​ − 1 ​ − 2 ​ ​ ​ 5 ​ − 2 ​ 2 ​... View the full answer

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