True/False: If and are both bases of the vector space , then the matrix sends
vectors in -coordinates to the corresponding vectors in -coordinates.

Consider two bases and for a vector space . Suppose that and .

- (a)
- What is the change-of-coordinates matrix ?

- (b)
- If is a vector in -coordinates, what is the corresponding vector in
-coordinates?

- (c)
- What is the change-of-coordinates matrix ?