Deep understanding by solving a problem posted:

If you start from what matrix does Ax is that A transform x in old basis separately to new basis (expressed still in old basis) then stretch by coefficient forming x.

So to solve above problem it is important to understand what the problem is:

IT’s not about solving the problem but a general approach to solve hard-to-wrap-around problem like this: grasp the concept, and interpret fine and subtle meaning of each word. What does it really mean?!