Consider the matrix $A$ below. First, show that $A$ is diagonalizable by computing the geometric multiplicities of the eigenvalues and quoting the relevant theorem. Second, find a diagonal matrix $D$ and a nonsingular matrix $S$ so that $\similar{A}{S}=D$. (See Exercise EE.C20 for some of the necessary computations.) \begin{equation*} A= \begin{bmatrix} 18 & -15 & 33 & -15\\ -4 & 8 & -6 & 6\\ -9 & 9 & -16 & 9\\ 5 & -6 & 9 & -4 \end{bmatrix} \end{equation*}