Okay, so my final is tomorrow. Thanks to HallsofIvy and Isomorphism I got rid of some confusion but I still lack knowledge on a few more problems. Any help would be greatly appreciated.

1. Let A = $\displaystyle 1/2 \begin{bmatrix}1&1\\1&1\end{bmatrix}$ and define $\displaystyle T:R^2 \rightarrow R^2$ by T(X)=AX. Describe geometrically what effect T has on $\displaystyle R^2$ by describing T(C), where C is the unit circle in $\displaystyle R^2$. (using eigenvectors)

2.a)Given $\displaystyle T:R^2\rightarrow R^2$ is linear and T(1,2) = (2,4) and T(2,0) = (0,0), graph T(F) (the image of F under T), where F is the set of points in $\displaystyle R^2$ located on the boundary of the triangle determined by the points (1,2), (2,0), and (0,0).

(I don't know how one would go about graphing so maybe some guidance as to how I'd do so for this problem would be nice)

b)Graph T(G), where G is the set of points strictly inside the triangle F. (In other words, G is the set of points not in F, but bounded by F.) [u](same applies for this problem)

.doc attached with those 2 questions along with one more.

Thanks again.