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.
Fig: 1