Mathematics - Determinant Question with Solution | TestHub

$\begin{array}{l}3x+5y+\lambda z=3\\ 7x+11y-9z=2\\ 97x+155y-189z=\mu \\ 93x+155y+31\lambda z=93\\ 97x+155y-189z=\mu \\ -++-\\ -4x+(31\lambda +189)z=93-\mu \\ 1085x+1705y-1395z=310\\ 1067x+1705y-2079z=11\mu \\ -+-\\ 18x+684z=310-11\mu \end{array}$ $\begin{array}{rl}& -36x+9(31\lambda +189)z=9(93-\mu )\\ & 36x+1368z=2(310-11\mu )\\ & (279\lambda +3069)z=1457-31\mu \end{array}$ for infinite solutions - $\begin{array}{rl}& \lambda =\frac{-3069}{279}=\frac{-341}{31}\\ & \mu =\frac{1457}{31}\end{array}$ $\mu +2\lambda =\frac{1457-682}{31}=\frac{775}{31}=25$