1. The problem statement, all variables and given/known data How do I know if this linear transformation is invertible or not? T: [ x ] ---> [ 2y ] [ y ] [ x-3y ] (I also uploaded a small .bmp file to represent this if this looks too ugly) 3. The attempt at a solution Well, I thought maybe it could be represented by a transformation matrix T [ 0 2 ] [ 1 -3 ] So then I just took the inverse of T, which I got as [ 1.5 1 ] [ 0.5 0 ] So does that mean that in the question, it is invertible? Because if it is, I'm getting the impression that these R2 to R2 linear transformations are invertible. Would this impression be correct?