Unformatted text preview: [3 marks] ax 1 + x 2 = 1 ax 1 + x 2 = a 2 (c) [1 bonus mark] x 2 1 + ax 2 2 = a ax 2 1 + x 2 2 = a 4 3. Let A = ± a b c d ² and I = ± 1 1 ² . (a) [3 marks] Prove that if adbc 6 = 0, then A has reduced rowechelon form I . (b) [2 marks] Prove that if A has reduced rowechelon form I , then adbc 6 = 0. (c) [1 bonus mark] The product of two 2 × 2 matrices is deﬁned thus: ± a b c d ²± A B C D ² = ± aA + bC aB + bD cA + dC cB + dD ² . Prove that the set S = ³± a b c d ² : adbc 6 = 0 ´ is closed under multiplication; that is, prove that the product of any two members of the set is itself in the set....
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