JEE Main 2020 (Online) 4th September Evening ShiftQuestion 1
If the system of equations $x+y+z=2$, $2x+4y-z=6$, $3x+2y+\lambda z=\mu$ has infinitely many solutions, then :
Determinant
Solution
$\begin{vmatrix}1&1&1\\2&4&-1\\3&2&\lambda\end{vmatrix}=0\Rightarrow\lambda=\tfrac92$. $\begin{vmatrix}1&1&2\\2&4&6\\3&2&\mu\end{vmatrix}=0\Rightarrow\mu=5$. $2\lambda+\mu=9+5=14$. Option (D).