Matrices & Determinants
Infinite Solutions — Two Parameters
nta_pyq_2024_apr
Grade 12
Question:
If the system of equations $2x+7y+\lambda z=3$, $3x+2y+5z=4$, $x+\mu y+32z=-1$ has infinitely many solutions, then $\lambda-\mu$ is equal to ________.
Step-by-Step Solution
Key Concept: Set $D=D_1=D_2=D_3=0$. From $D_3=0$: $\mu=-39$. From $D=0$: $\lambda=-1$.
$\lambda=-1$, $\mu=-39$. $\lambda-\mu=38$.
Correct Answer: 38