MATA23H3 Final: MATA23 Final Exam 2011 Solutions
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If a, b, c r3 show that a (b c) = Solution: let a = [a1, a2, a3], b = [b1, b2, b3], c = [c1, c2, c3] Lhs = a (b c) = [a1, a2, a3] . The system is ax = b where a = 2 (cid:12)(cid:12)(cid:12)(cid:12)(cid:12)(cid:12) 2 (cid:12)(cid:12)(cid:12)(cid:12)(cid:12)(cid:12) 5 (cid:12)(cid:12)(cid:12)(cid:12)(cid:12)(cid:12) 2 5 (cid:12)(cid:12)(cid:12)(cid:12)(cid:12)(cid:12) 2. It has pivots in columns 1 and 2 so columns 1 and 2 of a form a basis for its column space: 7/2s 6t (cid:12)(cid:12)(cid:12)(cid:12)(cid:12) s, t r. Mata23s page 2: [7 points] find a basis for the row space, a basis for the column space and a basis for the null space of a and verify the rank equation. The nonzero rows of h for a basis for the row space of a. Basis for a row space of a = { [1, 0, 7/2, 6] , [0, 1, 3/2, 3] }
