How do I determine the standard matrix of this transformation?

T([2,1]) = [3,-1] and T([-1,-1]) = [0,2]

(these are vertical 2x1 matrices)

create T as [[a,b],[b,c]] then multiply it by the first vector. This will give you 2 equations and 4 unknowns. Then repeat the process with the second vector, giving you 2 more equations. You should know what to do when you have 4 equations and 4 unknowns.

Just look at what is happening between the two column vectors, t is doing a simple transformation

http://s14.postimg.org/nlwmasugx/image.jpg

This is step by step