Visualization of the Axiom 3a

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