Problem 04 (a) What can be said about the four fundamental subspaces when Az = b has an unique solution, no solution, and infinitely many solutions? (b) Find the basis and dimension for each of the spaces formed by the following matrices. Also explain why they are vector spaces. (i) All diagonal 3 x 3 matrices. (ii) All symmetric 3 x 3 matrices (A = AT). (iii) All 3 x 3 skew-symmetric matrices (A7 = A). () Suppose A is the sum of two rank one matrices: A = uv\" + wz": (1) Which vectors span the column space of A? (ii) Which vectors span the row space of A? (iii) Under what conditions (if any) is the rank of A less than 27 (d) Express A as the sum of two rank one matrices where 3 3 R | A=l e 7 4