Linear Algebra Done Right · Problem 1C.19

Finite-Dimensional Vector Spaces — Sheldon Axler

Mathematics — Linear Algebra · sums-of-subspaces

Problem

Prove or give a counterexample: If

V_1, V_2, U

are subspaces of

V

such that

V_1 + U = V_2 + U,

then

V_1 = V_2