linear transformation, is diagonalizable? all values of a?

53 Views Asked by At

People i have the next problem. Let $f: \mathbb R_3 → \mathbb R_3$ be the linear transformation such that https://i.stack.imgur.com/qLTqd.png with $\mathcal B = \{(1,0, −1), (0,0,1), (0,1 , 0)\}$. The set of all values of $a \in \mathbb R$ such that $f$ is diagonalizable is.... and they give me a few options:

1)$\mathbb R−\{−2\}$

2)$\{−4\}$

3)$\mathbb R−\{−4\}$

4)$\{−2\}$

I have started to diagonalize the matrix, but when I try to diagonalize I can't find the roots because there is a parameter:/