math 235 hw6 - Homework 6, Due April 15 Adam Gamzon Related...

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Unformatted text preview: Homework 6, Due April 15 Adam Gamzon Related reading: sections 4.2, 4.3, 6.1, and 6.2 from the text 1. Let T : P 2 R 3 be the linear transformation defined by T ( f ) = f (2) f (3) f (4) . Let = 1 1 , 3 1 5 , 1 be a basis of R 3 and let = { 1 , 1 + x, 1 + x 2 } be a basis of P 2 . (a) Determine [ T ] . Solution: Note that T (1) = 1 1 , T (1+ x ) = 3 1 5 , and T (1+ x 2 ) = 5 6 17 . Write each of T (1) ,T (1+ x ) , and T (1+ x 2 ) as a linear combination of the basis vectors 1 1 , 3 1 5 , 1 in order to determine that the -coordinate vector of each one is [ T (1)] = 1 , [ T (1 + x )] = 1 and [ T (1 + x 2 )] = - 13 6 . Therefore, [ T ] = 1 0- 13 0 1 6 0 0 . (b) Find det([ T ] )....
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This note was uploaded on 11/22/2011 for the course MATH 255 taught by Professor Staff during the Spring '10 term at UMass (Amherst).

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math 235 hw6 - Homework 6, Due April 15 Adam Gamzon Related...

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