JEE Main 2020 (Online) 4th September Morning ShiftQuestion 1
If the system of equations $x-2y+3z=9$, $2x+y+z=b$, $x-7y+az=24$, has infinitely many solutions, then $a-b$ is equal to ________.
Determinant
Answer$5$
Solution
Coefficient determinant $=5a-40=0\Rightarrow a=8$. Consistency: $\begin{vmatrix}1&-2&9\\2&1&b\\1&-7&24\end{vmatrix}=0\Rightarrow b=3$. $a-b=5$.