Question

If the determinant of the matrix \[ \begin{vmatrix} 1 & 2 \\ 3 & x \end{vmatrix} \] is equal to $-2$, then the value of $x$ is:

• A. $2$
• B. $4$
• C. $6$
• D. $8$

Hint:

For every $2\times2$ determinant: \[ \begin{vmatrix} a & b c & d \end{vmatrix} =ad-bc \] Multiply diagonally and subtract.

Answer 1

The Correct Option is B

Concept: For a matrix \[ \begin{vmatrix} a & b \\ c & d \end{vmatrix}, \] the determinant is: \[ ad-bc \]

Step 1: Applying the determinant formula.
Given: \[ \begin{vmatrix} 1 & 2 \\ 3 & x \end{vmatrix} =-2 \] Therefore: \[ (1)(x)-(2)(3)=-2 \] \[ x-6=-2 \]

Step 2: Solving for $x$.
Add $6$ on both sides: \[ x=-2+6 \] \[ x=4 \] Hence, \[ \boxed{x=4} \]