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  4. The existence of the unique solution of the system x +y +z=λ, 5 x-y+μ z=10, 2 x+3 y-z=6 depends on

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Q. The existence of the unique solution of the system $x +y +z=\lambda,\, 5 x-y+\mu z=10,\, 2 x+3 y-z=6$ depends on

ManipalManipal 2011

Solution:

For unique solution of the given system, $\Delta \neq 0$
i.e. $\begin{vmatrix}1 & 1 & 1 \\ 5 & -1 & \mu \\ 2 & 3 & -1\end{vmatrix} \neq 0$
Hence, it depends only on $\mu$.