To calculate the determinant of the matrix A:
[tex]\[
A = \begin{pmatrix}
2 & -3 \\
-1 & 4
\end{pmatrix}
\][/tex]
The determinant of a 2x2 matrix of the form:
[tex]\[
\begin{pmatrix}
a & b \\
c & d
\end{pmatrix}
\][/tex]
is given by the formula:
[tex]\[
\text{det}(A) = ad - bc
\][/tex]
For our matrix A:
[tex]\[
a = 2, \quad b = -3, \quad c = -1, \quad d = 4
\][/tex]
Substituting these values into the formula, we get:
[tex]\[
\text{det}(A) = (2 \cdot 4) - (-3 \cdot -1)
\][/tex]
[tex]\[
= 8 - 3
\][/tex]
[tex]\[
= 5
\][/tex]
So, the determinant of the matrix A is:
[tex]\[
\boxed{5}
\][/tex]
