(a) What is meant by an eigenvector and the corresponding eigenvalue of a matrix $A$ ?

(b) Let $A$ be the matrix

$$A=\left(\begin{array}{ccc} 3 & -2 & -2 \\ 1 & 0 & -2 \\ 3 & -3 & -1 \end{array}\right)$$

Find the eigenvalues and the corresponding eigenspaces of $A$ and determine whether or not $A$ is diagonalisable.