JEE Main 2020 (Online) 8th January Morning ShiftQuestion 1
For which of the following ordered pairs $(\mu,\delta)$, the system of linear equations $x+2y+3z=1$, $3x+4y+5z=\mu$, $4x+4y+4z=\delta$ is inconsistent ?
Determinant
Solution
$R_2-R_1=(2,2,2)$ so $R_3=(4,4,4)=2(R_2-R_1)$ on the left. Consistent iff $\delta=2(\mu-1)$. $(1,0)$: $0=0$ ok. $(3,4)$: $4=4$ ok. $(4,3)$: $2(3)=6\ne3$, inconsistent. $(4,6)$: $6=6$ ok. Option (C).