Let V be a vector space over F, and let U and W be subspaces of V. The sum of U and W, denoted by U+W, is the subset U + W = {u+w: u € U, w € W}. Prove that U + W is a subspace of V.

Let a = Let V be the space formed by all vectors orthogonal to a. Show that V is a subspace of R?.

2. Let V be a vector space over F, and let U and W be subspaces of V. The sum of U and W, denoted by U + W, is the subset U + W = {u+w: u € U, w€ W}. Prove that U + W is a subspace of V.