Page 477 - Elementary_Linear_Algebra_with_Applications_Anton__9_edition

(a) If V is a subspace of and W is a subspace of V , then is a subspace of .
(b) for all vectors u, v, and w in an inner product space.
(c) If u is in the row space and the nullspace of a square matrix A, then .
(d) If u is in the row space and the column space of an matrix A, then .

Let have the inner product that was defined in Example 7
38.

of Section 6.1. Describe the orthogonal complement of
(a) the subspace of all diagonal matrices
(b) the subspace of symmetric matrices

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