Find a 2x2 matrix A and a vector v in R2 such that the transforma-

tion x --> Ax + v maps the triangle with vertices (1, 1); (2, -1);

(3, 4) into the triangle with vertices (0, 0); (1, 0); (0, 1). How

many different pairs (A, v) will do the job?

For the first part, it's pretty easy. Just find A and v s.t. (1,1) -> (0,0), (2,-1) -> (1,0) etc. Second part I haven't really thought about yet

If I see it correctly, the number of possible solutions should become obvious when you solve the problem as you get a system of linear equations with six real-valued unknowns (four in A and two in v) and six equations (one for each coordinate mapped).