Question

Find the determinant of the matrix: \[ \left| \begin{matrix} 10 & 4 \\ 13 & 5 \end{matrix} \right| \]

• A. 102
• B. 2
• C. -2
• D. -102

Hint:

For a 2x2 matrix \( \left[ \begin{matrix} a & b
c & d \end{matrix} \right] \), the determinant is calculated as \( ad - bc \).

Answer 1

The Correct Option is C

We are given the matrix: \[ \left| \begin{matrix} 10 & 4 \\ 13 & 5 \end{matrix} \right| \] The determinant of a 2x2 matrix is calculated as: \[ \text{det} \left( A \right) = ad - bc \] For the given matrix: \[ \left| \begin{matrix} 10 & 4 \\ 13 & 5 \end{matrix} \right| \] The determinant is: \[ (10 \times 5) - (4 \times 13) = 50 - 52 = -2 \] Thus, the correct answer is \( -2 \).