Q. The system of equations $x+y+z=6$, $x+2y+5z=9$, $x+5y+\lambda z=\mu$, has no solution if
A) $\lambda=15,\ \mu\ne17$
B) $\lambda\ne17,\ \mu\ne18$
C) $\lambda=17,\ \mu\ne18$
D) $\lambda=17,\ \mu=18$
Explanation
[Solution by Dr. Abubacker] The determinant is $\begin{vmatrix}1&1&1\\1&2&5\\1&5&\lambda\end{vmatrix}=\lambda-17$, so for $\lambda=17$ the coefficient rows are dependent: $R_3=-3R_1+4R_2$. Consistency then needs $\mu=-3(6)+4(9)=18$. So there is no solution for $\lambda=17,\ \mu\ne18$. Answer (3).
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.