Question

Find the determinant of the matrix: $$ \begin{bmatrix} 3 & 2 \\ 1 & 5 \end{bmatrix} $$

• A. 13
• B. 11
• C. 15
• D. 17

Hint:

For a 2x2 matrix, compute the determinant using \( ad - bc \), where \( a, b, c, d \) are the matrix elements in their respective positions.

Answer 1

The Correct Option is A

Given: \[ A = \begin{bmatrix} 3 & 2 \\ 1 & 5 \end{bmatrix} \] Step 1: Formula for Determinant
For a 2x2 matrix \( \begin{bmatrix} a & b \\ c & d \end{bmatrix} \), the determinant is: \[ \det(A) = ad - bc \] Step 2: Substitute the Values
Identify \( a = 3 \), \( b = 2 \), \( c = 1 \), \( d = 5 \). Compute: \[ \det(A) = (3 \cdot 5) - (2 \cdot 1) = 15 - 2 = 13 \] Thus, the determinant is: \[ \boxed{13} \]