9. The matrix A is defined by

$\displaystyle \mathbf{A} = \begin{bmatrix} \lambda+1 & 1 & \lambda \\ 1 & 2 & \lambda\\2 & \lambda & 1 \end{bmatrix}$

a. {done this part just proving $\displaystyle \mathbd{A}$ is singular when $\displaystyle \lambda$ = 1}

b. Now consider the system of equations:

$\displaystyle \mathbf{AX}=\mathbf{B}$

where

$\displaystyle \mathbf{X}=\begin{bmatrix}x\\y\\z \end{bmatrix} \; ; \; \mathbf{B} = \begin{bmatrix}2\\3\\2 \end{bmatrix}$

(i) Given that $\displaystyle \lambda = 1$, show that these equations are consistent and find their general solution.