16.-Linear-Algebra-by-Kenneth-Hoffman · Problem 2.2.7

Vector Spaces

Mathematics — Linear Algebra · union-of-subspaces

Problem

Let

W_1

and

W_2

be subspaces of a vector space

V

such that the set-theoretic union of

W_1

and

W_2

is also a subspace. Prove that one of the spaces

W_i

is contained in the other.