Determinants
In the sketch below is shown two vectors, the determinant of the matrix formed by the two vectors, a blue square, and a red image parallelogram.
Be certain to drag the vertices of the image around!
How is the determinant related to the area of the two quadrilaterals?
What happens when the vectors point in the same direction?
What happens when the vectors point in the opposite direction?
What happens when the vectors are perpendicular?
What happens when the vectors make an angle of 45°?
What happens when the determinant is negative?
What happens when the determinant is zero?