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a$)$ Find the dominant eigenvalue and a corresponding eigenvector using power method.

$\left[\begin{array}{ccc}4& 2& 3\\ 2& 7& 6\\ 3& 6& 4\end{array}\right]$

Perform $3$ iteration only. Keep $4$ places after decimal. Take $x_0=[1,1,1{]}^T.$

b$.)$ Find inverse of the matrix given below using Cayley Hamilton's Theorem

$\left[\begin{array}{ccc}4& 0& 1\\ -2& 1& 0\\ -2& 0& 1\end{array}\right]$

c$.)$ Find an example two subspaces A and B of V such that AUB is not a subspaces of V$.$

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