Use the steps below to prove the following relations among the four fundamental subspaces determined by an m X n matrix A.
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 AT)⊥.
