If the system of linear equations $x + ay + z = 3$,$x + 2y + 2z = 6$,and $x + 5y + 3z = b$ has no solution,then:

The number of solutions of the equations $x + y - z = 0$,$3x - y - z = 0$,and $x - 3y + z = 0$ is

If $A = \begin{bmatrix} -1 & 2 \\ 2 & -1 \end{bmatrix}$ and $B = \begin{bmatrix} 3 \\ 1 \end{bmatrix}$,$AX = B$,then $X = $

If the system of equations
$ 11 x+y+\lambda z=-5 $
$ 2 x+3 y+5 z=3 $
$ 8 x-19 y-39 z=\mu $
has infinitely many solutions,then $ \lambda^4-\mu $ is equal to :

The number of $3 \times 3$ matrices $A$,whose entries are either $1$ or $-1$ and for which the system $A\begin{bmatrix} x \\ y \\ z \end{bmatrix} = \begin{bmatrix} 1 \\ -1 \\ 0 \end{bmatrix}$ has exactly three distinct solutions,is

If $[x]$ is the greatest integer less than or equal to $x$ and $|x|$ is the modulus of $x$,then the system of three equations $\begin{aligned} & 2x + 3|y| + 5[z] = 0, \\ & x + |y| - 2[z] = 4, \\ & x + |y| + [z] = 1 \end{aligned}$ has