The system of linear equations $x + y + z = 2$, $2x + y - z = 3,$ $3x + 2y + kz = 4$has a unique solution if

The values of $\lambda$ and $\mu$ for which the system of linear equations

$x+y+z=2$

$x+2 y+3 z=5$

$x+3 y+\lambda z=\mu$

has infinitely many solutions are, respectively

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

The value of $k \in R$, for which the following system of linear equations

$3 x-y+4 z=3$

$x+2 y-3 x=-2$

$6 x+5 y+k z=-3$

has infinitely many solutions, is:

Number of values of $m$ for which the lines $x + y - 1 = 0$, $(m - 1) x + (m^2 - 7) y - 5 = 0 \,\,\&\,\, (m - 2) x + (2m - 5) y = 0$ are concurrent, are

The system of equations $\lambda x + y + z = 0,$ $ - x + \lambda y + z = 0,$ $ - x - y + \lambda z = 0$, will have a non zero solution if real values of $\lambda $ are given by