2. Recall that in class we proved the following theorem: Theorem. Let T: VW be a linear transformation between finite-dimensional inner product spaces, and let T*: W → V be the adjoint of T. Then N(T) and R(T*) are orthogonal complementary pair in V, and R(T) and N(T*) are orthogonal complementary pair in W. Use this theorem to derive the following corollary: Corollary. Let A E Mmxn (R). Then the row space of A and the solution space of Ax = 0 are orthogonal complementary pair in R", and the column space of and the solution space of Aty = 0 are orthogonal complementary pair in Rm.

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