TS EAMCET · Maths · Determinants
If the homogeneous system of linear equations
\(x-2 y+3 z=0,2 x+4 y-5 z=0,3 x+\lambda y+\mu z=0 \text { has }\)
non-trivial solution, then \(8 \mu+11 \lambda=\)
- A \(2\)
- B \(6\)
- C \(-6\)
- D \(-2\)
Answer & Solution
Correct Answer
(B) \(6\)
Step-by-step Solution
Detailed explanation
Condition for non-trivial solution \(|A|=0\) \(\left|\begin{array}{ccc}1 & -2 & 3 \\ 2 & 4 & -5 \\ 3 & \lambda & \mu\end{array}\right|=0\) \(4 \mu+5 \lambda+2(2 \mu+15)+3(2 \lambda-12)=0 \Rightarrow 8 \mu+11 \lambda=6\).
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