Question

The value of $\lambda$ for which the system of equations $2x - y - z = 12$, $x - 2y + z = - 4,x + y + \lambda z = 4$ has no solution is

• A. 3
• B. –3
• C. 2
• D. –2

Answer 1

Answer: (D)

–2

Answer 2

$D = \left| \begin{matrix} 2 & - 1 & - 1 \\ 1 & - 2 & 1 \\ 1 & 1 & \lambda \end{matrix} \right| = - 3\lambda - 6$. For no solution the necessary condition is $- 3\lambda - 6 = 0 \Rightarrow \lambda = - 2$. It can be see that for $\lambda = - 2$, there is no solution for the given system of equations.