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Question 4 -2 -6 24 -20 0 2 Let A = -2 -3 9 -14 0 5 4 9 -33 34 3 -13 -2 -3 9 -14 -3 11 It is given that the reduced row-echelon forms of A and AT are respectively 0 0 0 3 4 0 010 0 0 1 -5 2 0 1 0 0 0 01 -2 and 0 01 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 O 0 0 O (i) Write down rank(A), nullity(A), rank(AT) and nullity(AT). (ii) Find a basis for the nullspace of A. (iii) Express the 1st row of A as a linear combination of other rows of A. (iv) Find columns of A that form a basis S for the column space of A, and express other columns of A as linear combinations of vectors in S. (v) Find rows of A that form a basis T for the row space of A, and extend T to a basis for Re