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

We are given the matrix \( A = \begin{bmatrix} 2 & 1
3 & 4 \end{bmatrix} \), and we need to find the determinant of matrix \( A \). Step 1: Use the formula for the determinant of a 2x2 matrix The determinant of a 2x2 matrix \( \begin{bmatrix} a & b
c & d \end{bmatrix} \) is given by: \[ \text{det}(A) = ad - bc \] Step 2: Substitute the values from matrix \( A \) For the given matrix \( A = \begin{bmatrix} 2 & 1
3 & 4 \end{bmatrix} \), we have \( a = 2 \), \( b = 1 \), \( c = 3 \), and \( d = 4 \). \[ \text{det}(A) = (2)(4) - (1)(3) = 8 - 3 = 5 \] Answer: The determinant of matrix \( A \) is \( 5 \), so the correct answer is option (2).