Question

The value of the determinant \( \Delta = \begin{vmatrix} 1 & 4 & 3 \\ 0 & 12 & 9 \\ 1 & 2 & 2 \end{vmatrix} \) is:

• A. 2
• B. 4
• C. 6
• D. 8

Hint:

To calculate a 3x3 determinant, use cofactor expansion or perform row operations to simplify the determinant.

Answer 1

The Correct Option is A

Step 1: Use cofactor expansion or any method to compute the determinant. The determinant is given by: \[ \Delta = 1 \times \begin{vmatrix} 12 & 9 \\ 2 & 2 \end{vmatrix} - 4 \times \begin{vmatrix} 0 & 9 \\ 1 & 2 \end{vmatrix} + 3 \times \begin{vmatrix} 0 & 12 \\ 1 & 2 \end{vmatrix}. \] Step 2: After calculation, we find \( \Delta = 2 \).

Final Answer: \[ \boxed{2} \]