JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
The system of equations
\(\begin{aligned}
& x+y+z=6 \\
& x+2 y+5 z=9, \\
& x+5 y+\lambda z=\mu,
\end{aligned}\) has no solution if
- A \(\lambda=15, \mu \neq 17\)
- B \(\lambda \neq 17, \mu \neq 18\)
- C \(\lambda=17, \mu \neq 18\)
- D \(\lambda=17, \mu=18\)
Answer & Solution
Correct Answer
(C) \(\lambda=17, \mu \neq 18\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & \mathrm{D}=\left|\begin{array}{lll}1 & 1 & 1 \\ 1 & 2 & 5 \\ 1 & 5 & \lambda\end{array}\right|=0 \\ & \lambda=17 \\ & D_z=\left|\begin{array}{lll}1 & 1 & 6 \\ 1 & 2 & 9 \\ 1 & 5 & \mu\end{array}\right| \neq 0 \\ & \mu \neq 18\end{aligned}\)
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