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

If $\begin{bmatrix} 3 & 1 \\ 4 & 1 \end{bmatrix} X = \begin{bmatrix} 5 & -1 \\ 2 & 3 \end{bmatrix}$,then $X =$

Consider the system of equations: $ax + by + cz = 2$, $bx + cy + az = 2$, $cx + ay + bz = 2$, where $a, b, c$ are real numbers such that $a + b + c = 0$. Then, the system

If the system $\begin{bmatrix} 2 & 8 \\ 3 & 7 \end{bmatrix} \begin{bmatrix} a \\ b \end{bmatrix} = k \begin{bmatrix} a \\ b \end{bmatrix}$ has a non-trivial solution, then the positive value of $k$ and a solution of the system for that value of $k$ are:

If $x = a$,$y = b$,$z = c$ is a solution of the system of linear equations $x + 8y + 7z = 0$,$9x + 2y + 3z = 0$,and $x + y + z = 0$ such that the point $(a, b, c)$ lies on the plane $x + 2y + z = 6$,then $2a + b + c$ equals

Examine the consistency of the system of equations: $x+2y=2$ and $2x+3y=3$.