Ordered pair (a, b) , for which system of linear equations 3 x-2 y+z=b ; 5 x-8 y+

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3 and 4 .Determinants and Matrices

medium

The ordered pair $(a, b)$, for which the system of linear equations $3 x-2 y+z=b$ ; $5 x-8 y+9 z=3$ ; $2 x+y+a z=-1$ has no solution, is

A

$\left(3, \frac{1}{3}\right)$

B

$\left(-3, \frac{1}{3}\right)$

C

$\left(-3,-\frac{1}{3}\right)$

D

$\left(3,-\frac{1}{3}\right)$

(JEE MAIN-2022)

Solution

$\left|\begin{array}{ccc} 3 & -2 & 1 \\ 5 & -8 & 9 \\ 2 & 1 & a \end{array}\right|=0$

$3(-8 a-9)+2(5 a-18)+1(21)=0$

$\Rightarrow a=-3$

Also $\Delta_{2}=\left|\begin{array}{ccc}3 & -2 & b^{\frac{1}{3}} \\ 5 & 8 & 3 \\ 2 & 1 & -1\end{array}\right|$

If $b =\frac{1}{3}$

$\Delta_{2}=0$

So $b$ must be equal to $-\frac{1}{3}$

Standard 12

Mathematics

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