JEE Main 2021 (Online) 1st September Evening ShiftQuestion 1
Consider the system of linear equations
$-x+y+2z=0$
$3x-ay+5z=1$
$2x-2y-az=7$
Let $S_1$ be the set of all $a\in R$ for which the system is inconsistent and $S_2$ be the set of all $a\in R$ for which the system has infinitely many solutions. If $nS_1$ and $nS_2$ denote the number of elements in $S_1$ and $S_2$ respectively, then
Determinant
Solution
$\Delta=-(a-3)(a-4)$. For $a=3$ and $a=4$ the augmented rank is $3$ while the coefficient rank is $2$, so the system is inconsistent: $nS_1=2$, $nS_2=0$.