True/False: Let be a linear transformation. The matrix for relative to the bases
and for and respectively is given by:
where .

True/False: Let be a linear transformation. Let and be bases for and respectively.
Let be the matrix for relative to and . Then which of the following equations is
true?

Let and be bases for the vector spaces and respectively. Let be a linear
transformation. Given the equations below, find the matrix for relative to and
.

Let and be bases for the vector spaces and respectively. Let be a linear
transformation. Given the equations below, find the matrix for relative to and
.

Let be a basis for some vector space . If the linear transformation sends vectors
written with respect to the basis to vectors written with respect to the basis , then
the matrix for relative to (or the -matrix for ) satisfies: