Calculate the dterminant

Question

5 -2
-1 3

Answer 1

To calculate the determinant of a \(2 \times 2\) matrix, we use the formula:

\[ \text{det} \begin{pmatrix} a & b \ c & d \end{pmatrix} = ad - bc \]

For the given matrix:

\[ \begin{pmatrix} 5 & -2 \ -1 & 3 \end{pmatrix} \]

we have:

• \(a = 5\)
• \(b = -2\)
• \(c = -1\)
• \(d = 3\)

Now, applying the formula:

\[ \text{det} = (5)(3) - (-2)(-1) \] \[ \text{det} = 15 - 2 \] \[ \text{det} = 13 \]

Thus, the determinant of the matrix is \(13\).