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Unformatted text preview: 1 and rotating 1 by 3 2 radians yields 1 . Thus, T ( e 1 ) = T 1 = 1 T ( e 2 ) = T 1 = 1 Hence, the standard matrix for T is [ T ( e 1 ) T ( e 2 ) ] = 11 . 3. (2.2.24) Suppose A is n n and the equation A x = b has a solution for each b in n . Explain why A must be invertible. [ Hint: Is A row equivalent to I n ?] Since A x = b has a solution for each b in n , we can solve each of the n matrix equations A u 1 = e 1 A u 2 = e 2 A u n = e n Thus, A [ u 1 u 2 u n ] = [ A u 1 A u 2 A u n ] = [ e 1 e 2 e n ] = I . This means that the matrix B = [ u 1 u 2 u n ] satisFes AB = I , which implies that A is invertible....
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This note was uploaded on 04/23/2008 for the course MATH 20F taught by Professor Buss during the Spring '03 term at UCSD.
 Spring '03
 BUSS
 Linear Algebra, Algebra, Vectors

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