Matrices & Determinants
Infinite Solutions — Finding Parameters
nta_pyq_2024_apr
Grade 12
Question:
If the system of equations $11x+y+\lambda z=-5$, $2x+3y+5z=3$, $8x-19y-39z=\mu$ has infinitely many solutions, then $\lambda^4-\mu$ is equal to:
Step-by-Step Solution
Key Concept: For infinite solutions: $D=0$ (gives $\lambda$) and $D_1=0$ (gives $\mu$).
$\lambda=-2$, $\mu=-31$. $\lambda^4-\mu=16+31=47$.
Correct Answer: 3