Question

If \( A = \begin{bmatrix} 2 & 1
3 & 4 \end{bmatrix} \), then the determinant of matrix \( A \) is:

• A. \( 4 \)
• B. \( 5 \)
• C. \( 7 \)
• D. \( 10 \)

Hint:

For a 2x2 matrix, use the formula \( \text{det}(A) = ad - bc \) to quickly calculate the determinant.

Answer 1

The Correct Option is B

The determinant of matrix \( A = \begin{bmatrix} 2 & 1
3 & 4 \end{bmatrix} \) is to be calculated. Step 1: Apply the 2x2 matrix determinant formula For a matrix \( \begin{bmatrix} a & b
c & d \end{bmatrix} \), the determinant is calculated as: \[ \text{det}(A) = ad - bc \] Step 2: Input values from matrix \( A \) For \( A = \begin{bmatrix} 2 & 1
3 & 4 \end{bmatrix} \), \( a=2 \), \( b=1 \), \( c=3 \), and \( d=4 \). \[ \text{det}(A) = (2)(4) - (1)(3) = 8 - 3 = 5 \] Answer: The determinant of matrix \( A \) is \( 5 \).