JEE Main 2024 (Online) 1st February Morning ShiftQuestion 1
If the system of equations
$2x+3y-z=5$
$x+\alpha y+3z=-4$
$3x-y+\beta z=7$
has infinitely many solutions, then $13\alpha\beta$ is equal to
Determinant
Solution
$\Delta=0$ and the other determinants vanish for infinitely many solutions; solving gives $\alpha=-70,\ \beta=-\frac{16}{13}$. $13\alpha\beta=13\cdot(-70)\cdot\left(-\frac{16}{13}\right)=1120$. Option B.