Find the value of `|(8,4),(5,6)|`.

Options

A. 38
B. 28
C. 10
D. 12

Answer

To find the value of the determinant represented by the matrix \(\begin{pmatrix} 8 & 4 \\ 5 & 6 \end{pmatrix}\), we can use the formula for the determinant of a 2x2 matrix:

\[ \text{det} \begin{pmatrix} A & B \\ C & D \end{pmatrix} = AD - BC \]

In this case, we have:

- \(A = 8\)
- \(B = 4\)
- \(C = 5\)
- \(D = 6\)

Now, we can substitute these values into the determinant formula:

1. **Calculate \(AD\)**:
\[ AD = 8 \times 6 = 48 \]

2. **Calculate \(BC\)**:
\[ BC = 4 \times 5 = 20 \]

3. **Subtract \(BC\) from \(AD\)**:
\[ \text{det} = AD - BC = 48 - 20 = 28 \]

Thus, the value of the determinant \(|(8,4),(5,6)|\) is \(28\).