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23. (a) Compute the eigenvalues of each of the following matrices. (i) $\left[\begin{array}{ll}4 & 0 \\ 2 & 2\end{array}\right]$ (ii) $\left[\begin{array}{ll}1 & 2 \\ 3 & 4\end{array}\right]$ (iii) $\left[\begin{array}{ll}2 & 1 \\ 2 & 3\end{array}\right]$ (iv) $\left[\begin{array}{rr}4 & -1 \\ 1 & 2\end{array}\right]$ (v) $\left[\begin{array}{rrr}0 & 2 & 1 \\ 3 & -1 & -3 \\ -2 & 2 & 3\end{array}\right]$ (b) Determine an eigenvector associated with the largest eigenvalue, using the method in Example 4, for the matrices in part (a).

Please show ALL work no matter how small the step is.

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