Linear Algebra Done Right · Problem 3E.15

Linear Maps — Sheldon Axler

Mathematics — Linear Algebra · quotient-spaces

Problem

Suppose

U

is a subspace of

V

and

v_1 + U, \ldots, v_m + U

is a basis of

V/U

and

u_1, \ldots, u_n

is a basis of

U

. Prove that

v_1, \ldots, v_m, u_1, \ldots, u_n

is a basis of

V