Matrices & Determinants
System of Equations — No Solution Condition
nta_pyq_2026_jan
Grade 12
Question:
If the system of equations
$3x+y+4z=3$
$2x+\alpha y-z=-3$
$x+2y+z=4$
has no solution, then the value of $\alpha$ is equal to:
Step-by-Step Solution
Key Concept: For no solution, $\Delta=0$ but at least one of $\Delta_x,\Delta_y,\Delta_z\neq0$. Set $\Delta=\begin{vmatrix}3&1&4\\2&\alpha&-1\\1&2&1\end{vmatrix}=0$.
$\alpha=19$.
Correct Answer: 1