Question

If $\left| \begin{matrix} x^{2} + x & x + 1 & x - 2 \\ 2x^{2} + 3x - 1 & 3x & 3x - 3 \\ x^{2} + 2x + 3 & 2x - 1 & 2x - 1 \end{matrix} \right| = Ax - 12$, then the value of A is.

• A. 12
• B. 24
• C. –12
• D. – 24

Answer 1

Answer: (B)

24

Answer 2

Sol. Trick : Put $x = 1$, then we have

\mathbf{2} & \mathbf{2} & \mathbf{-}\mathbf{1} \\ \mathbf{4} & \mathbf{3} & \mathbf{0} \\ \mathbf{6} & \mathbf{1} & \mathbf{1} \end{matrix} \right|\mathbf{= A}\mathbf{-}\mathbf{12}\mathbf{\Rightarrow}\left| \begin{matrix} \mathbf{0} & \mathbf{2} & \mathbf{-}\mathbf{1} \\ \mathbf{1} & \mathbf{3} & \mathbf{0} \\ \mathbf{5} & \mathbf{1} & \mathbf{1} \end{matrix} \right|\mathbf{= A}\mathbf{-}\mathbf{12}$$ **{**Apply $C_{1} \rightarrow C_{1} - C_{2}$**}** $\Rightarrow$ $- 2 + ( - 1)( - 14) = A - 12 \Rightarrow A = 24$.