Assuming that R_2, and R_1 are linearly indepdent. If for any . Since R_1 is lin independent, we are assured some x(unique) exists in our global coordinate system. So , again an inverse also exists for , call it . So . So, x is in our global coordinate sys and we know how to get from our global coordinates to B, so , so to get from A to B, we have will do the transformation