WBJEE · Maths · Determinants
The system of linear equations \(\lambda x+y+z=3\)
\(x-y-2 z=6\)
\(-x+y+z=\mu\) has
- A infinite number of solutions for \(\lambda \neq-1\) and all \(\mu\)
- B infinite number of solutions for \(\lambda=-1\) and \(\mu=3\)
- C no solution for \(\lambda, x-1\)
- D unique solution for \(\lambda=-1\) and \(\mu=3\)
Answer & Solution
Correct Answer
(B) infinite number of solutions for \(\lambda=-1\) and \(\mu=3\)
Step-by-step Solution
Detailed explanation
Augmented matrix [A:B] = \(\left[\begin{array}{rrrr}1 & -1 & -2 & 6 \\ -1 & 1 & 1 & \mu \\ \lambda & 1 & 1 & 3\end{array}\right]\) \(\sim\left[\begin{array}{cccc}1 & -1 & -2 & 6 \\ 0 & 0 & -1 & \mu+6 \\ \lambda+1 & 0 & -1 & 9\end{array}\right]\) Applying…
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