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
JEE · Math · previous-year question
- A.$\lambda=17, \mu=18$
- B.$\lambda=17, \mu \neq 18$correct
- C.$\lambda=15, \mu \neq 17$
- D.$\lambda \neq 17, \mu \neq 18$
Answer
B. $\lambda=17, \mu \neq 18$
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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