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Task 1:
You must use the given vectors and . The only things that you can adjust are the weights and by moving the sliders left and right.
(a) Can you find weights such that is the vector (8,1)?
(b) Are your weights from (a) unique, or are there other choices?
(c) Are you able to get to any point on the plane using the given vectors?
If there are other choices, what is another choice?
(d) Can you find weights such that is the zero vector?
Task 2:
Now you may choose your own vectors and by sliding the blue and green vertices, respectively. You can also still adjust the weights and by moving the sliders left and right.
(a) Can you give an example of a linear combination that resulted in the zero vector that did not have 0's for the weights.
(b) What is interesting about your vectors and from (b)?