- Thread starter
- #1

I need some help with this question...

I have a mtrix A:

[tex]\begin{pmatrix} k &-2 &1 \\ 4 &-k &2 \\ 0 &0 &1 \end{pmatrix}[/tex]

and I need to find for which values of k, the matrix is diagonalized. I know the way to check if a matrix is diagonalized is to check the algebraic and geometric multipliers, but technically, how to do it with a parameter is beyond my skill, I need some help with the solution. I found the characteristic polynomial, it is:

[tex]-\lambda ^{3}+\lambda ^{2}+k ^{2}\lambda-k ^{2}+8-8\lambda[/tex]

and the final answer should be a^2>8 AND a!=3 (not equal 3)

Thanks !!