Linear Algebra Done Right · Problem 1C.14

Finite-Dimensional Vector Spaces — Sheldon Axler

Mathematics — Linear Algebra · sums-of-subspaces

Problem

Suppose

U = \{(x, -x, 2x) \in \mathbf{F}^3 : x \in \mathbf{F}\} \quad \text{and} \quad W = \{(x, x, 2x) \in \mathbf{F}^3 : x \in \mathbf{F}\}.

Describe

U + W

using symbols, and also give a description of

U + W

that uses no symbols.