Question

If \( A = \begin{bmatrix} 2 & 3 \\ 1 & 4 \end{bmatrix} \), find the determinant of \( A \).

• A. \( 5 \)
• B. \( 6 \)
• C. \( 7 \)
• D. \( 8 \)

Hint:

To find the determinant of a 2x2 matrix \( \begin{bmatrix} a & b
c & d \end{bmatrix} \), use the formula \( ad - bc \).

Answer 1

The Correct Option is A

The matrix is given as: \[ A = \begin{bmatrix} 2 & 3 \\ 1 & 4 \end{bmatrix} \] The determinant of a 2x2 matrix \( \begin{bmatrix} a & b \\ c & d \end{bmatrix} \) is calculated as \( ad - bc \). For matrix \( A \): \[ a = 2, \ b = 3, \ c = 1, \ d = 4 \] \[ \det(A) = (2 \cdot 4) - (3 \cdot 1) = 8 - 3 = 5 \] Thus, the determinant of \( A \) is: \[ {5} \]