The existence of the unique solution of the system of equations: x + y + z = λ 5x − y + µz = 10 2x + 3y − z = 6 depends on

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(a) µ only 	ext{ For a unique solution, }\left| A ight|
eq 0 \Rightarrow \begin{vmatrix}1 & 1 & 1 \ 5 & - 1 & \mu \ 2 & 3 & - 1\end{vmatrix} 
eq 0 \Rightarrow 1\left( 1 - 3\mu ight) - 1\left( - 5 - 2\mu ight) + 1\left( 15 + 2 ight) 
eq 0 \Rightarrow 1 - 3\mu + 5 + 2\mu + 17 
eq 0 \Rightarrow - \mu + 23 
eq 0 \Rightarrow \mu 
eq 23 	ext{ So, existence of a unique solution depends only on }\mu.

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