Matrices & Determinants
Infinite Solutions Condition
nta_pyq_2025_apr
Grade 12
Question:
If the system of equations $2x - y + z = 4$, $5x + \lambda y + 3z = 12$, $100x - 47y + \mu z = 212$ has infinitely many solutions, then $\mu - 2\lambda$ is equal to:
Step-by-Step Solution
Key Concept: Set $\Delta_z = 0$ to find $\lambda$, then set $\Delta_y = 0$ to find $\mu$.
From $\Delta_z = 0$: $\lambda = -2$. From $\Delta_y = 0$: $\mu = 53$. $\mu - 2\lambda = 53 - 2(-2) = 57$.
Correct Answer: 57