Q$1.$ Find the dominant eigen value and corresponding eigen vector using power methed.

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

Perform $3$ iteration only. Keep $4$ places after decimal. Take

$x_0=[1,1,1{]}^T.$

b$)$ Find unverse of the matrix given below using cayley Hamilton's Theorm

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

C$)$ Find an example two subspaces A and $B$ of $V$ such that $AB$ is not a subspace of $V$