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

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