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