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Study Stuff for MCA Examinations - NIMCET
Study Stuff for MCA Examinations - NIMCET
Previous Year Question (PYQs)
The system of equations
$3x + y + 4z = 3$
$2x + ay - z = -3$
$x + 2y + z = 4$
has no solution, then the value of $\alpha$ is equal to:
Solution
for no solution $\Delta = 0$
$\begin{vmatrix} 3 & 1 & 4 \ 2 & \alpha & -1 \ 1 & 2 & 1 \end{vmatrix} = 0$
$\Rightarrow 3(\alpha + 2) + 1(-1 - 2) + 4(4 - \alpha) = 0$
$\Rightarrow 3\alpha + 6 - 3 + 16 - 4\alpha = 0$
$\Rightarrow 19 - \alpha = 0 \Rightarrow \alpha = 19$
$\Delta_x = \begin{vmatrix} 3 & 1 & 4 \ -3 & \alpha & -1 \ 4 & 2 & 1 \end{vmatrix}$
$\neq 0$
$\therefore$ no solution for $\alpha = 19$
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