Matrices & Determinants
System Classification — Identifying False Option
nta_pyq_2023_apr
Grade 12
Question:
For the system $2x+4y+2az=b$, $x+2y+3z=4$, $2x+5y+2z=8$, which of the following is NOT correct?
It has unique solution if $a=b=6$
It has infinitely many solutions if $a=3, b=6$
It has infinitely many solutions if $a=3, b=8$
It has unique solution if $a=b=8$
Step-by-Step Solution
Key Concept: $\Delta=-18(a-3)$. For $a=3$: $\Delta=0$. Check $\Delta_3=9(b-8)$. Infinite solutions need $\Delta=\Delta_3=0$, i.e., $a=3$ and $b=8$.
$a=3,\ b=6$: $\Delta=0,\ \Delta_3\neq0\Rightarrow$ no solution. Option (2) is false.
Correct Answer: 2