Linear Algebra Done Right · Problem 1C.7

Finite-Dimensional Vector Spaces — Sheldon Axler

Mathematics — Linear Algebra · subspaces

Problem

Prove or give a counterexample: If

U

is a nonempty subset of

\mathbf{R}^2

such that

U

is closed under addition and under taking additive inverses (meaning

-u \in U

whenever

u \in U

), then

U

is a subspace of

\mathbf{R}^2