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Lab_7_SolutionsRuth

# Lab_7_SolutionsRuth - Lab#7(week of 1 In 3 find the matrix...

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Math 115 SE Lab #7 (week of October 27, 2008) 1. In 3 , find the matrix for each of the following linear transformations: a) the projection of = z y x X onto the line 1 L through the origin with direction vector = 1 0 1 1 d ; Using the above diagram, we know that ( ) ( ) = + + = + = + + = = = z y x z x z x z x z y x d d d X X proj U d 1 0 1 0 0 0 1 0 1 2 1 0 2 1 1 0 1 2 1 0 1 1 0 1 1 , 0 , 1 , , 2 2 2 2 Therefore, the matrix = 1 0 1 0 0 0 1 0 1 2 1 1 A gives = = w v u z y x A z y x T 1 1 , the projection of z y x onto 1 L . b) the projection of = z y x X onto the line 2 L through the origin with direction vector ⎡− = 1 0 1 2 d ; Using a similar development to a), with ⎡− = 1 0 1 2 d , we have X=[ x , y,z ] L U=[ u , v,w ] y z x

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Math 115 SE ( ) ( ) ( ) = + = ⎡− + = ⎡− + + = = = z y x z x z x z x z y x d d d X X proj U d 1 0 1 0 0 0 1 0 1 2 1 0 2 1 1 0 1 2 1 0 1 1 0 1 1 , 0 , 1 , , 2 2 2 2 Therefore, the matrix
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Lab_7_SolutionsRuth - Lab#7(week of 1 In 3 find the matrix...

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