A2_soln - Math 235 Assignment 2 Solutions 1. Determine the...

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Unformatted text preview: Math 235 Assignment 2 Solutions 1. Determine the matrix of the linear operator L : R 3 → R 3 with respect to the basis B and determine [ L ( ~x )] B where B = { ~v 1 ,~v 2 ,~v 3 } , L ( ~v 1 ) = 2 ~v 1- ~v 2- 3 ~v 3 , L ( ~v 2 ) = 4 ~v 1 + 3 ~v 2- ~v 3 , L ( ~v 3 ) =- ~v 2 and ( ~x ) B = (2 ,- 1 ,- 1). Solution: To determine the matrix of L with respect to B , we need the B-coordinates of the images of the basis vectors. We have [ L ( ~v 1 )] B = (2 ,- 1 ,- 3) , [ L ( ~v 2 )] B = (4 , 3 ,- 1) , [ L ( ~v 3 )] B = (0 ,- 1 , 0) . Hence, the matrix of L with respect to B is [ L ] B = [ L ( ~v 1 )] B [ L ( ~v 2 )] B [ L ( ~v 3 )] B = 2 4- 1 3- 1- 3- 1 . Thus [ L ( ~x )] B = [ L ] B [ ~x ] B = 2 4- 1 3- 1- 3- 1 2- 1- 1 = - 4- 5 . 2. Assume each of the following matrices is the matrix of some linear transformation with respect to the standard basis. Determine the matrix of the linear transformation with respect to the given basis B ....
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This note was uploaded on 04/18/2010 for the course MATH 235 taught by Professor Celmin during the Spring '08 term at Waterloo.

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A2_soln - Math 235 Assignment 2 Solutions 1. Determine the...

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