(Solved): 4) Describe the characteristic polynomial of a diagonal matrix. Compute the characteristic polynomi ...

4) Describe the characteristic polynomial of a diagonal matrix. Compute the characteristic polynomial of the following matrices to develop/test your answer. Verify the Cayley-Hamilton Theorem for these examples. You can quickly create these matrices with diag ( $$\left[\begin{array}{lll}2& 2& 1\end{array}\right])$$ (a) $$\left(\begin{array}{ll}2& 0\\ 0& 1\end{array}\right)$$ (b) $$\left(\begin{array}{lll}2& 0& 0\\ 0& 2& 0\\ 0& 0& 1\end{array}\right)$$ (c) $$\left(\begin{array}{llll}2& 0& 0& 0\\ 0& 2& 0& 0\\ 0& 0& 1& 0\\ 0& 0& 0& 1\end{array}\right)$$ (d) $$\left(\begin{array}{lll}2& 0& 0\\ 0& 1& 0\\ 0& 0& 3\end{array}\right)$$