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Unformatted text preview: Simon Fraser University School of Engineering Science ENSC 483  Modern Control Systems Spring 2007–Assignment 2 1. Consider the following set of vectors: v 1 = 1 1 2 3 ; v 2 = 2 2 1 ; v 3 = 1 1 3 . 5 ; v 4 =  . 5 4 . 5 5 . 5 Define two basis B 1 = { v 1 , v 2 } , and B 2 = { v 3 , v 4 } for the subspace span of { v 1 , v 2 , v 3 , v 4 } . (a) Find the transformation matrix T , which transforms vectors represented in B 1 into vectors represented in B 2 basis. (b) Find the representation of the vector v = [1 3 4 2] T in the B 1 basis. (c) Use the results of a) to find the representation of v with respect to B 2 basis. (d) Verify that your answer in c) is correct. 2. Consider the following vectors in ( < 3 , < ) x 1 =  2 1 2 ; x 2 = 1 1 1 ; x 3 = 8 5 7 and following vectors in (...
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 Spring '07
 MehrdadSaif
 Linear Algebra, Standard basis, Matrix representation, Modern Control Systems, School of Engineering Science

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