JEE Main 2024 (Online) 9th April Morning ShiftQuestion 1
Let $\lambda,\mu\in\mathbf{R}$. If the system of equations
$3x+5y+\lambda z=3$
$7x+11y-9z=2$
$97x+155y-189z=\mu$
has infinitely many solutions, then $\mu+2\lambda$ is equal to :
Determinant
Solution
$\Delta=\begin{vmatrix}3&5&\lambda\\7&11&-9\\97&155&-189\end{vmatrix}=0\Rightarrow\lambda=-11$. $\begin{vmatrix}3&5&3\\7&11&2\\97&155&\mu\end{vmatrix}=0\Rightarrow\mu=47$ (rank check: both ranks 2). $\mu+2\lambda=47-22=25$. Option C.