Orthogonal Complements: Prove the properties stated in Problems 1-2 using the following definition, illustrated by Fig. 3.5.4. Assume that V is a subspace of Rn.
Let V be a subspace of Rn. A vector uÌ… is orthogonal to subspace V provided that uÌ… is orthogonal to every vector in V. The set of all vectors in Rn that are orthogonal to V is called the orthogonal complement of V, denoted
v”´ = {uÌ… ( Rn | uÌ… ( vÌ… = 0 for every vÌ… ( V}.

Figure 3.5.4 An orthogonal complement uÌ… to a plane V
1. V”´ is a subspace of Rn.
2. V ˆ© V”´ = {0Ì…}

V