Matrices & Determinants
Infinite Solutions — Finding Parameters
nta_pyq_2023_apr
Grade 12
Question:
If the system of equations $x+y+az=b$, $2x+5y+2z=6$, $x+2y+3z=3$ has infinitely many solutions, then $2a+3b$ is equal to
Step-by-Step Solution
Key Concept: For infinitely many solutions, $\Delta=0$ and $\Delta_1=0$. Compute $\Delta$ and $\Delta_1$ as determinants of the coefficient and augmented matrices.
$a=7,\ b=3$. $2a+3b=23$.
Correct Answer: 3