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Unformatted text preview: âˆš 3/2 âŽ¦ â€¢ Then the matrix associated to T 1 is A1 : 1/(3/4 + 1/4) âŽ¡ âˆš 3/2 1/2, âŽ¤ âŽ£ â€“Â½ âˆš 3/2 âŽ¦ 24.3 Example â€“ If S and T are two 11 linear maps show that ( S Â° T )1 = T1 Â° S 1 . Solution. â€¢ Let A and B be the two matrices induced by S and T respectively. â€¢ Since both S and T are 11 then both A x = 0 and B x = 0 have unique solutions and so they are both invertible. (Previous result) â€¢ Since A and B are both invertible then A1 is induced by S 1 and B 1 is induced by T1 . (Previous result) â€¢ Furthermore AB is invertible and so ( AB ) 1 is induced by ( S Â° T )1 . â€¢ Since T1 Â° S 1 ( x ) = B 1 A1 ( x ) = ( AB )1 ( x ) = ( S Â° T )1 ( x ) for all x . â€¢ Then ( S Â° T )1 = T1 Â° S 1 ....
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 Winter '08
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 Linear Algebra, Matrices, Invertible Matrices, linear transformation mapping

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