Thread: Reduce the following quadratic form to canonical form.

I encountered next and the last problem from algebra, I hope you will be able to help me, because my books aren't enough to explain this for me

Reduce the following quadratic form to canonical form. Express the new variables in terms of
the old ones.
f(x, y, z) = x^2 + 4y^2 + 3z^2 + 4xy − 6xz + 4yz

Originally Posted by brianbrian

I encountered next and the last problem from algebra, I hope you will be able to help me, because my books aren't enough to explain this for me

Reduce the following quadratic form to canonical form. Express the new variables in terms of
the old ones.
f(x, y, z) = x^2 + 4y^2 + 3z^2 + 4xy − 6xz + 4yz

There are several ways to solve the problem, Gauss method, orthogonal diagonalization, elementary transformatios (rows and columns),... .What method have you covered?

So this should be solved as matrix? I am familliar with gauss method.