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Im having a problem with deciphering positive definite and negative definite for this quadratic form i determined from a matrix.

I dont quite understand how to evaluate if its pos def or neg def.

From what I see in my notes, q(x,y) > 0 for all x not equal to 0. This doesnt help much as with some terms being squared and some not, im not sure if q will always be positive. I also dont know if there is anything different being a 3-variable quadratic. Anyways here it is:

1. The problem statement, all variables and given/known data

q(x, y, z) = 2x² - 2xy + y² - 8yz – 2xz + 5z²

2. Relevant equations

q(x,y) > 0 for all x not equal to 0

Any help is appreciated

Thanks

Chris

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# Homework Help: 3 variable quadratic

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