Can you please find the Eigenvalues and eigenvectors of this expression p(x,y,z)= 3x^2+y^2+2z^2-2xy+2xz-2yz ?

Question

1. 

Answer 1

Here's a start:

[x,y,z] [3 -1 1 ] [x] = x(Transpose)• Ax

[1 1 -1 ] [y]

[1 -1 2 ] [z]

Not symmetric--will have to orthogonally diagnolize...

Is it diagnolizable?? Find characteristic equation ((v = [x,y,z]^T

Pv=Det( [3-λ -1 1 ] ) = Good luck with silly errors :)

[-1 -λ -1 ]

[1 -1 2-λ]