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Choose the correct option.
The system of linear equations x + y + z = 6, x + λ y + 2z = 7 and 3x + y + z = 12 has a unique…
The system of linear equations $x + y + z = 6$, $x + \lambda y + 2z = 7$ and $3x + y + z = 12$ has a unique solution if:
- a$\lambda = 2$
- b$\lambda \neq 2$
- c$\lambda = -2$
- d$\lambda \neq -2$
Answer
Answer
Correct option: b
Answer: (b) $\lambda \neq 2$
$\begin{vmatrix}1&1&1\\1&\lambda&2\\3&1&1\end{vmatrix}=(\lambda-2)-1(1-6)+(1-3\lambda)=4-2\lambda$. A unique solution needs the determinant to be non-zero, so $\lambda\neq 2$.