Instructions

1. Answer the questions related to vector spaces and subspaces.
2. Provide proofs where necessary.
3. Submit your answers in the portal.

Problem 1

Determine if the following set is a subspace of $\mathbb{R}^3$: $W = \{ (x, y, z) \in \mathbb{R}^3 : x + y + z = 0 \}$