JEE Main 2020 (Online) 7th January Evening ShiftQuestion 1
If the system of linear equations,
$x+y+z=6$
$x+2y+3z=10$
$3x+2y+\lambda z=\mu$
has more than two solutions, then $\mu-\lambda^2$, is equal to
Determinant
Answer$13$
Solution
Infinitely many solutions need $\Delta=0$ and consistency: $R_3=4R_1-R_2$ forces $\lambda=1$ and $\mu=24-10=14$. Then $\mu-\lambda^2=13$.