Question

i need to solve the following system to get the eigenvectors: 0 -5 0
-5 0 0
-1 1 -5 , in term of s and/or t
can anyone help

Answer 1

Ah I think the matrix has been messed up when you wrote the question. Should it be:
\[A=\left[\begin{matrix} 0& -5 & 0\\ -5 & 0& 0\\-1 & 1 & -5 \end{matrix}\right]\]?
I called the matrix A to make it simpler to explain.
Are you familiar with the method of \[|A-\lambda I|=0\]
For eigenvalues lambda?

Answer 2

Yes. I have \[\lambda \] = 1 and 6. For 6 I get vectors /110/ and /001/. But i am not sure about matrix A for 1. I get /110/, but then the it will not be eigenspace then with 2 vectors the same?

Answer 3

I will check it out now and see what I get.

Answer 4

i keep on loosing connection. the actual quastion is to proof that matrix A is diagonalizable

Answer 5

i have \[\lambda \] += 1 and six. for 6 , i get vectors /110/ and / 001/, but then i anm not sure about lambda = 1