Question:
If the system of equations
$x+y+z=2 \quad 2 x+4 y-z=63 x+2 y+\lambda z=\mu$
has infinitely many solutions, then :
Correct Option: , 4
Solution:
$\left|\begin{array}{ccc}1 & 1 & 1 \\ 2 & 4 & -1 \\ 3 & 2 & \lambda\end{array}\right|=0 \quad[\because$ Equation has many solutions $]$
$\Rightarrow-15+6+2 \lambda=0 \Rightarrow \lambda=\frac{9}{2}$
$\therefore D_{Z}=\left|\begin{array}{llc}1 & 1 & 2 \\ 2 & 4 & 6 \\ 3 & 2 & 2 \mu\end{array}\right|=0 \Rightarrow \mu=5$
$\therefore 2 \lambda+\mu=14$