2. Let T: R" → R" be a linear transformation. Let S = {₁,...,Un} be a basis for R", and let A

denote the matrix representation for T with respect to the basis S. Finally, let Š = {₁,...,Un}

be another basis for R".

a. We can define a matrix CE Rxn relating the two basis by

Cuivi, for all i = 1,..., n.

=

Show that C is invertible.

b. If à denotes the matrix representation of T with respect to the basis Š, find a simple formula

for à involving the matrices A and C, and check that it is correct (should only take one or two

lines).

c. Use this formula and properties of the determinant to show that

det Ã

= det A.