Question:
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:
Correct Option: , 3
Solution:
$D=\left|\begin{array}{lll}1 & 1 & 1 \\ 1 & 2 & 3 \\ 1 & 3 & \lambda\end{array}\right|=0 \Rightarrow \lambda=5$
$D_{x}=\left|\begin{array}{lll}2 & 1 & 1 \\ 5 & 2 & 3 \\ \mu & 3 & 5\end{array}\right|=0 \Rightarrow \mu=8$
Click here to get exam-ready with eSaral
For making your preparation journey smoother of JEE, NEET and Class 8 to 10, grab our app now.