Permutation of Matrices on a Vector

[Andrew Yang]

If you have two matrices, ?=((1,0),(1,1))A and ?=((1,1),(0,1)) and you take any combination of them and multiply them by a vector ?=⟨6,15⟩, what possible new vectors can you get? I've spent a long time trying this out, but I can't find a pattern. I was able to see one, though, when I did ?=⟨1,1⟩: https://math.stackexchange.com/questions/4028354/permutation-of-matrices-on-a-vector.