If the system of linear equations

 2x + 3y – z = -2

x + y + z = 4

$x-y+\left|\lambda \right|z=4\lambda -4$  

where  $\lambda \in R,$  has no solution, then

If $A\left[\begin{array}{ccc}\hfill 1\hfill & \hfill 0\hfill & \hfill 1\hfill \end{array}\right]=2\left[\begin{array}{ccc}\hfill 1\hfill & \hfill 0\hfill & \hfill 1\hfill \end{array}\right]$ <!-- [if gte mso 9]><xml> </xml><![endif]-->, <!-- [if gte mso 9]><xml> </xml><![endif]-->  $A\left[\begin{array}{ccc}\hfill -1\hfill & \hfill 0\hfill & \hfill 1\hfill \end{array}\right]=4\left[\begin{array}{ccc}\hfill -1\hfill & \hfill 0\hfill & \hfill 1\hfill \end{array}\right]$ and $A\left[\begin{array}{ccc}\hfill 0\hfill & \hfill 1\hfill & \hfill 0\hfill \end{array}\right]=2\left[\begin{array}{ccc}\hfill 1\hfill & \hfill 0\hfill & \hfill 0\hfill \end{array}\right]$ <!-- [if gte mso 9]><xml> </xml><![endif]--> where, A is a 3 × 3 matrix and (A –3I) $\left[\begin{array}{ccc}\hfill x\hfill & \hfill y\hfill & \hfill z\hfill \end{array}\right]=\left[\begin{array}{ccc}\hfill -1\hfill & \hfill 2\hfill & \hfill 3\hfill \end{array}\right]$ <!-- [if gte mso 9]><xml> </xml><![endif]--> then the value of (x, y, z) is

Let $M=\left[\begin{array}{cc}\hfill 0\hfill & \hfill -\alpha \hfill \\ \hfill \alpha \hfill & \hfill 0\hfill \end{array}\right],$ where a is a non-zero real number an $N={\displaystyle \sum _{k=1}^{49}{M}^{2k}.}$  If (I – M²)N = -2I, then the positive integral value of α is…………….

Let $A=\left(\begin{array}{cc}\hfill 2\hfill & \hfill -1\hfill \\ \hfill 0\hfill & \hfill 2\hfill \end{array}\right).$ If $B=I{-}^5\text{?}{C}_1\left(adjA\right){+}^5\text{?}{C}_2{\left(adjA\right)}^2-..{.}^5\text{?}{C}_5{\left(adjA\right)}^5,$  then the sum of all elements of the matrix B is

Let $A=\left(\begin{array}{cc}\hfill 2\hfill & \hfill -1\hfill \\ \hfill 0\hfill & \hfill 2\hfill \end{array}\right).$ If $B=I{-}^5\text{?}{C}_1\left(adjA\right){+}^5\text{?}{C}_2{\left(adjA\right)}^2-..{.}^5\text{?}{C}_5{\left(adjA\right)}^5,$  then the sum of all elements of the matrix B is

If the system of equations

x + 6y + 6z = $\lambda x$ $$

4x – y + 4z = $\lambda y$ $$

$2\lambda x+2\lambda y+\lambda z=5z$

has non-trivial solution then the value of $\left|\lambda \right|$ $$ equals (where $\lambda \in$ $$ R)