If the system of equations  $x+2 y+3 z=3$  ; $4 x+3 y-4 z=4$ ; $8 x+4 y-\lambda z=9+\mu$ has infinitely many solutions, then the ordered pair $(\lambda, \mu)$ is equal to

If ${a_1}x + {b_1}y + {c_1}z = 0,{a_2}x + {b_2}y + {c_2}z = 0$ ${a_3}x + {b_3}y + {c_3}z = 0$ and $\left| {\,\begin{array}{*{20}{c}}{{a_1}}&{{b_1}}&{{c_1}}\\{{a_2}}&{{b_2}}&{{c_2}}\\{{a_3}}&{{b_3}}&{{c_3}}\end{array}\,} \right| = 0,$then the given system has

Solve system of linear equations, using matrix method. $x-y+z=4$ ; $2 x+y-3 z=0$ ; $x+y+z=2$

Solve the system of the following equations  $\frac{2}{x}+\frac{3}{y}+\frac{10}{z}=4$ ; $\frac{4}{x}-\frac{6}{y}+\frac{5}{z}=1$  ; $\frac{6}{x}+\frac{9}{y}-\frac{20}{z}=2$

The number of values of $k$ for which the system of linear equations, $(k + 2) x + 10y = k,\,\,kx + (k + 3)y = k – 1$  has no solution, is