i would be very thankful if someone could help me on this question, i know how to do the first bit but the last two questions confuse me a little. thanks in advance
$M = \left( \begin{smallmatrix} 8&40&-30\\ 25&98&-75\\ 35&140&-107 \end{smallmatrix} \right)$
Let $v = [1, 2, 3]^T$
Show that $v$ is an eigenvector for the matrix M and determine the associated eigenvalue, say $\lambda$.
Determine the dimension of the eigenspace, $E_\lambda$, of M.
It is known that 3 is also an eigenvalue of M. Quoting any general result you need, determine whether or not M is diagonalisable.