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