Determinants

In the sketch below is shown two vectors, the determinant of the matrix formed by the two vectors, a blue quadrilateral, and a red image quadrilateral.

  • 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?

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Steve Phelps, Created with GeoGebra