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3 and 4 .Determinants and Matrices
medium
If the system of equations
$x-2 y+3 z=9$
$2 x+y+z=b$
$x-7 y+a z=24$
has infinitely many solutions, then $a - b$ is equal to
A
$5$
B
$11$
C
$8$
D
$3$
(JEE MAIN-2020)
Solution
$D =\left|\begin{array}{ccc}1 & -2 & 3 \\ 2 & 1 & 1 \\ 1 & -7 & a \end{array}\right|=0 \Rightarrow a =8$
also, $D _{1}=\left|\begin{array}{ccc}9 & -2 & 3 \\ b & 1 & 1 \\ 24 & -7 & 8\end{array}\right|=0 \Rightarrow b =3$
hence, $a- b =8-3=5$
Standard 12
Mathematics