QJEEM24Mab859: JEE Main 2024 Mathematics - Class 12 JEEM24Mab859 Solution: Consider the system of linear equations , where . Then, which…

$\begin{aligned}& \left|\begin{array}{ccc}1 & 1 & 1 \\1 & 2 & \lambda^2 \\1 & 3 & \lambda\end{array}\right|=0 \\& \Rightarrow 2 \lambda^2-\lambda-1=0 \\& \lambda=1,-\frac{1}{2} \\& \left|\begin{array}{ccc}1 & 1 & 5 \\2 & \lambda^2 & 9 \\3 & \lambda & \mu\end{array}\right|=0 \Rightarrow \mu=13\end{aligned}$

Infinite solution $\lambda=1 \& \mu=13$

For unique $\operatorname{sol}^{\mathrm{n}} \lambda \neq 1$

For no $\operatorname{sol}^{\mathrm{n}} \lambda=1 \& \mu \neq 13$

If $\lambda \neq 1$ and $\mu \neq 13$

Considering the case when $\lambda=-\frac{1}{2}$ and $\mu \neq 13$ this will generate no solution case