Problem 2. (3 + 4 points) (i) If A has 7" pivot columns, then show that AT has 7" pivot columns too. Give an example of a 3 X 3 matrix A for which the pivot column positions are different for A and AT. (ii) If AB : 0, the show that the columns of B are in the nullspace of A. Use this to prove that if the matrices are square of size n, then rank(A) + rank(B) S n. Problem 3. (8 + 4 points) (i) Find an orthonormal basis {v1, V2, v3} of R3 such that v1, v2 spans the column space of the following matrix A = 2 (ii) What is the least square solution to Ax = b if b = (1 2 7) T