1. Find a 2 x 2 matrix that maps e1 to -e2 and e2 to e1+3e2.

2. Consider the linear transformation described by the matrix A..1@0&1)].Note that arbitrary points on the x-axis can be written as [(s@0)] for s R and arbitrary points on the y-axis can be written as [(0@t)] for t R. To what set of points does this transformation map the x-axis to? To what set of points does this transformation map the y-axis to?

3. Define the unit square as the collection of points in R^2 with vertices (0,0), (0,1), (1,0), and (1,1). Sketch the unit square.

4. For each of the following linear transformation matrices, sketch the transformation of the unit square.

A_1=[(2&0@1&1)],A_2=[(0&1@-1&0)],A_3=[(cos(/4)&-sin(/4)@sin(/4)&cos(/4))] 

5. Find a transformation matrix that maps the unit square to the parallelogram with vertices (0,0), (2,4), (1,3), and (3,7).