The values of $\lambda$ and $\mu$ for which the system of equations $x+y+z=6, x+2y+3z=10, x+2y+\lambda z=\mu$ has infinitely many solutions are

Let $k_1$ and $k_2$ be the maximum and minimum values of $k$ for which the system of equations $x + ky = 1$,$kx + y = 2$,and $x + y = k$ are consistent. Then $k_1^2 + k_2^2$ is equal to:

If $AX=B$,where $A=\left[\begin{array}{ccc}1 & -1 & 1 \\ 2 & 1 & -3 \\ 1 & 2 & 1\end{array}\right]$,$X=\left[\begin{array}{l}x \\ y \\ z\end{array}\right]$,and $B=\left[\begin{array}{l}4 \\ 0 \\ 2\end{array}\right]$,then find the value of $2x+y-z$.

For $\alpha, \beta \in R$,suppose the system of linear equations $x-y+z=5$,$2x+2y+\alpha z=8$,and $3x-y+4z=\beta$ has infinitely many solutions. Then $\alpha$ and $\beta$ are the roots of:

If $A$ is a matrix such that $\left[\begin{array}{ll} 2 & 1 \\ 3 & 2 \end{array}\right] A \left[\begin{array}{ll} 1 & 1 \end{array}\right] = \left[\begin{array}{ll} 1 & 1 \\ 0 & 0 \end{array}\right]$, then $A$ is equal to

Let $A=\left[\begin{array}{rr}2 & -1 \\ 3 & 4\end{array}\right], B=\left[\begin{array}{ll}5 & 2 \\ 7 & 4\end{array}\right], C=\left[\begin{array}{ll}2 & 5 \\ 3 & 8\end{array}\right]$. Find a matrix $D$ such that $CD-AB=O$.