(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Make a change of variable that transforms the quadratic form with no cross-product term:

9x1^2 - 8x1x2 = 3x2^2

2. Relevant equations

A = PDP^-1

Q = y^TDy

3. The attempt at a solution

I know the answer. This is a question regarding concept.

The eigenvalues for this problem are 1 and 11. The order in which I construct D affect the coefficients of the quadratic form following a change of variable.

Consider constructing D as either

1 0

0 11

or

11 0

0 1

The two resulting quadratic forms would have their coefficients switched.

Basically, I'm asking, is this ok?

Would both answers be acceptable?

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# Homework Help: Linear Algebra, Quadratic Forms, Change of Variable (concept)

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