Use the steps below to prove the following relations among the four fundamental subspaces determined by an m x n matrix A. Row A = (Nul A)^⊥ Col A = .NulA^T)?

a. Show that Row A is contained in (Nul A)^⊥, (Show that if x is in Row A, then x is orthogonal to every u in Nul A.)
b. Suppose rank A = r. Find dim (Nul A)^⊥ and dim (Nul A)^⊥, and then deduce from part (a) that Row A = (Nul A)^⊥?.

c. Explain why Col A = (Nul A^T)^⊥.