Scaling Property of Determinants

Visualization of the Axiom 3a
1. Double the length of one side of the parallelogram ABCD. (Set one of the sliders at 2 and the other one at 1). a) How does it affect its area? b) Write your answer with determinants’ notation. c) Compare the length and the direction of the vectors and (or and ). What is their relation to the determinant? 2. Double the lengths of both sides of the parallelogram . How does it affect a) its area? b) the entries in each row of the determinant? c) the value of the determinant? 3. Double one of the sides of the parallelogram and triple the other one. a) How does it affect its area? Write your answer with determinants’ notation. b) Compare the result to the previous exercise. c) Explore for other real numbers and generalize your answer. 4. Set both sliders at 1, B at (1,0) and D at (0,1). a) Which geometric figure is obtained? b) Which of the axioms for determinants is provided? 5. Can a determinant represent area of a rectangle? Investigate how!