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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 and I = 1 1 . (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 dened thus: a b c d A B C D = aA + bC aB + bD cA + dC cB + dD . Prove that the set S = a b c d : 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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 Spring '08
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 Math, Equations

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