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Unformatted text preview: R 2 ! R 3 , L ( x ) = ( x 1 x 2 1) T . (b) L : R 2 ! R 3 , L ( x ) = (0 0 x 1 x 2 ) T . (c) L : C [0 : 1] ! C [0 ; 1], L ( f ) = F where F ( x ) = R x f ( t ) dt and C [0 ; 1] is the vector space of all continuous functions on the interval [0 ; 1]. 6. Is it possible to construct a linear transformation ful±lling the following requirements? Describe the linear transformation if yes, or give an explanation if no. (a) T : R 2 ! R 2 , T ((1 0) T ) = (2 0) T , T ((0 1) T ) = (0 2) T , T ((1 1) T ) = (2 ± 2) T . (b) T : R 2 ! R 2 , T ((1 ± 1) T ) = (2 0) T , T ((2 ± 1) T ) = (0 2) T , T (( ± 3 2) T ) = ( ± 2 ± 2) T . (c) T : R 3 ! R 2 , T ((1 ± 1 1) T ) = (2 0) T , T ((1 1 1) T ) = (0 2) T . Find their standard matrix representations for the cases of linear transformations....
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This note was uploaded on 05/04/2011 for the course MATH 1111 taught by Professor Dr,li during the Spring '10 term at HKU.
 Spring '10
 Dr,Li

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