Linear Algebra Done Right · Problem 1C.6

Finite-Dimensional Vector Spaces — Sheldon Axler

Mathematics — Linear Algebra · subspaces

Problem

((a)) Is

\{(a, b, c) \in \mathbf{R}^3 : a^3 = b^3\}

a subspace of

\mathbf{R}^3

? ((b)) Is

\{(a, b, c) \in \mathbf{C}^3 : a^3 = b^3\}

a subspace of

\mathbf{C}^3