Hey there, im having problems with a question to do with transformations. Ive done part a) but part b) i have no idea :S

problem as follows

Consider the transformation T : R2 -> R2 where T (x1; x2) = (2x1 - x2; x1 - x2) :

(a) Write the transformation in matrix form: i.e.

|x'1| |? ? | |x1|

|x'2| = |? ? | |x2|

I.e., find A such that T (x) = Ax:

(b) Find the matrix B such that U (x) = Bx where U is the transformation U : R2 -> R2 given

by U (x1; x2) = (x1 + x2; x1)

(c) Use matrix multiplication to find expressions for (U o T) (x1; x2) and (T o U) (x1; x2) :

(d) Use matrices to find T^-1 (x1; x2) and U^-1 (x1; x2) or else explain why an inverse does not

exist.

Part a) simply is

t= |2 -1| |x1|

|1 -1| |x2|

after this no idea, help will be much appreciated