JEE Main 2025 (Online) 2nd April Evening ShiftQuestion 1
If the system of equations
$2x+\lambda y+3z=5$
$3x+2y-z=7$
$4x+5y+\mu z=9$
has infinitely many solutions, then $\left(\lambda^{2}+\mu^{2}\right)$ is equal to :
Determinant
Solution
$D_z=-(\mu+5)=0\Rightarrow\mu=-5$; $D_y=\lambda+1=0\Rightarrow\lambda=-1$; and $D=-3\lambda\mu-4\lambda+4\mu+31=-15+4-20+31=0$ holds. Ranks of coefficient and augmented matrices are both 2. $\lambda^2+\mu^2=1+25=26$. Option (C).