Question

Find the value of the determinant \( \begin{vmatrix} 2 & 3 \\ 4 & 5 \end{vmatrix} \).

• A. 2
• B. 1
• C. 0
• D. -1

Answer 1

The Correct Option is B

Step 1: Recall the formula for the determinant of a 2x2 matrix For a 2x2 matrix \( \begin{vmatrix} a & b \\ c & d \end{vmatrix} \), the determinant is given by: \[ \text{determinant} = ad - bc \] Step 2: Apply the formula to the given matrix For the matrix \( \begin{vmatrix} 2 & 3 \\ 4 & 5 \end{vmatrix} \), we have: - \( a = 2 \), - \( b = 3 \), - \( c = 4 \), - \( d = 5 \). Now, substitute these values into the determinant formula: \[ \text{determinant} = (2)(5) - (3)(4) = 10 - 12 = -2 \] Answer: Therefore, the value of the determinant is \( -2 \). So, the correct answer is option (4).