AP EAMCET · Maths · Determinants
If the system of simultaneous linear equations \(\mathrm{x}+\mathrm{y}+\mathrm{z}=\lambda, 5 \mathrm{x}-\mathrm{y}+\mu \mathrm{z}=10\) and \(2 \mathrm{x}+3 \mathrm{y}-\mathrm{z}=6\) has unique solution, then
- A \(\mu=23\) and \(\lambda \in \mathrm{R}\)
- B \(\mu \in \mathrm{R}\) and \(\lambda \neq 23\)
- C \(\mu \neq 23\) and \(\lambda \in \mathrm{R}\)
- D \(\mu=23\) and \(\lambda=16\)
Answer & Solution
Correct Answer
(C) \(\mu \neq 23\) and \(\lambda \in \mathrm{R}\)
Step-by-step Solution
Detailed explanation
Given system of equations \(x+y+z=\lambda\)...(i) \(5 x-y+\propto z=10\)...(ii) \(2 x+3 y-z=6\)...(iii) has unique solution \(\therefore\left|\begin{array}{rrc}1 & 1 & 1 \\ 5 & -1 & \mu \\ 2 & 3 & -1\end{array}\right| \neq 0\)…
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