tut3 - MATH 1104F - Solutions to Tutorial Assignment 3...

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Unformatted text preview: MATH 1104F - Solutions to Tutorial Assignment 3 February 2, 2010 1. Let T : R 2 R 2 be the linear transformation that rotates points through- 3 / 4 (clockwise). (a) Find the standard matrix for T . (b) Find T ( x 1 , x 2 ). Solution: (a) T ( e 1 ) = (- 2 / 2 ,- 2 / 2) and T ( e 2 ) = ( 2 / 2 ,- 2 / 2). Thus the standard matrix for T is A = [ T ( e 1 ) T ( e 2 ) ] = [- 2 / 2 2 / 2- 2 / 2- 2 / 2 ] . (b) A [ x 1 x 2 ] = [- 2 / 2 2 / 2- 2 / 2- 2 / 2 ][ x 1 x 2 ] = [- 2 2 x 1 + 2 2 x 2- 2 2 x 1- 2 2 x 2 ] Hence T ( x 1 , x 2 ) = (- 2 2 x 1 + 2 2 x 2 ,- 2 2 x 1- 2 2 x 2 ). 2. Let T : R 3 R 4 be the linear transformation defined by T ( x, y, z ) = ( x + 2 z, y- 3 z, x + 2 y- 4 z,- x + y- 5 z ) . (a) Find the image of (1 , 1 , 1). (b) Find a vector v in R 3 whose image under T is (- 1 , 5 , 9 , 6). (c) Is there more than one v whose image under T is (- 1 , 5 , 9 , 6)?...
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This note was uploaded on 03/22/2010 for the course MATH 1104 taught by Professor Unknown during the Winter '10 term at Carleton.

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tut3 - MATH 1104F - Solutions to Tutorial Assignment 3...

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