Determinant of a 2x2 Matrix

Determinant of a 2x2 Matrix

This sketch shows the connection between the determinant of a 2x2 matrix and the parallelogram. You can change the two vectors being used by either dragging their heads or by typing in coordinates for the head. Notice that the determinant matches the area of the parallelogram formed by the two vertices. If and are switched so the angle from the positive -axis to is smaller than that of , then the determinant will be negative. Notice in the determinant shown, the first row corresponds to the components of and the second row corresponds to the components of .