Given the matrix
[tex]\begin{bmatrix}{a} & {b} & {} \\ {c} & {d} & {}{}\end{bmatrix}[/tex]its determinant is computed as follows:
ad - cb
In this case, the matrix is
[tex]\begin{bmatrix}{2} & {-1} & \\ {4} & -5 & {}\end{bmatrix}[/tex]and its determinant is
2(-5) - 4(-1) = -10 - (-4) = -10 + 4 = -6
