If x 2 + x x + 1 x - 2 2 x 2 + 3 x - 1 3 x 3 x - 3 x 2 + 2 x + 3 2 x - 1 2 x - 1 = a x - 12 , then a is equal to:

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Question: Answered & Verified by Expert

If

|\begin{matrix} x^{2} + x & x + 1 & x - 2 \\ 2 x^{2} + 3 x - 1 & 3 x & 3 x - 3 \\ x^{2} + 2 x + 3 & 2 x - 1 & 2 x - 1 \end{matrix}| = a x - 12

, then

a

is equal to:

MathematicsDeterminantsJEE MainJEE Main 2015 (11 Apr Online)

Options:

A $- 24$
B $24$
C $- 12$
D $12$

Solution:

1267 Upvotes Verified Answer

The correct answer is:

24

Put

x = 1

on both the sides

|\begin{matrix} 2 & 2 & - 1 \\ 4 & 3 & 0 \\ 6 & 1 & 1 \end{matrix}| = a - 12

\Rightarrow 2 (3 - 0) - 2 (4 - 0) - 1 (4 - 18) = a - 12

\Rightarrow 6 - 8 + 14 = a - 12

\Rightarrow 12 = a - 12

\Rightarrow 24 = a .

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