Linear Algebra Done Right · Problem 3E.14

Linear Maps — Sheldon Axler

Mathematics — Linear Algebra · quotient-spaces

Problem

Suppose

U

and

W

are subspaces of

V

and

V = U \oplus W

. Suppose

w_1, \ldots, w_m

is a basis of

W

. Prove that

w_1 + U, \ldots, w_m + U

is a basis of

V/U