I am having problems trying to orthogonally diagonalise the below matrix. I am stuck at the stage where you find the eigenvalues.
The matrix is
5 -4 0
-4 3 -4 = 0
0 -4 1
This is what I get, but I cannot solve it so I think I have done something wrong.
5-λ -4 0
-4 3-λ -4 = 0
0 -4 1-λ
(5-λ)*|(3-λ)(1-λ) - (-4)(-4)| + 4*|(-4)(1-λ)| = 0
this works down to
(5-λ)(λ^2 +12λ - 29)
when typing this I have just realised that I just need to use the quadratic equation to solve (λ^2 +12λ - 29) and (5 - λ) is just λ = 5.
So if someone could just confirm if I'm heading towards the right direction or not, then that would be great