QJEEM22Mae70b: JEE Main 2022 Mathematics - Class 12 JEEM22Mae70b Solution: The ordered pair (a, b), for which the system of linear…

Question

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The ordered pair (a, b), for which the system of linear equations

3x $-$ 2y + z = b

5x $-$ 8y + 9z = 3

2x + y + az = $-$ 1

has no solution, is :

Accepted Answer

$| \begin{matrix} 3 & - 2 & 1 \\ 5 & - 8 & 9 \\ 2 & 1 & a \end{matrix} | = 0 \Rightarrow - 14 a - 42 = 0 \Rightarrow a = - 3$

Now 3 (equation (1)) $-$ (equation (2)) $-$ 2 (equation (3)) is

$3(3x - 2y + z - b) - (5x - 8y + 9z - 3) - 2(2x + y + az + 1) = 0$

$\Rightarrow - 3b + 3 - 2 = 0 \Rightarrow b = {1 \over 3}$

So for no solution $a = - 3$ and $b \ne {1 \over 3}$

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