This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
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 Bcoordinates 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 ....
View
Full
Document
This note was uploaded on 04/18/2010 for the course MATH 235 taught by Professor Celmin during the Spring '08 term at Waterloo.
 Spring '08
 CELMIN
 Math

Click to edit the document details