Matrices & Determinants
Infinite Solutions — Sum Expression
nta_pyq_2024_apr
Grade 12
Question:
Let $\lambda,\mu\in\mathbb{R}$. If the system of equations $3x+5y+\lambda z=3$, $7x+11y-9z=2$, $97x+155y-189z=\mu$ has infinitely many solutions, then $\mu+2\lambda$ is equal to:
Step-by-Step Solution
Key Concept: The third equation must be a linear combination of the first two. $97=31\cdot3+4$... use elimination. From solution: $\lambda=-341/31$ and $\mu=1457/31$.
$\mu+2\lambda=25$.
Correct Answer: 2