e483h2s_07 - ENSC 483 HW#2 SolutionM. Saif 1 Simon Fraser...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: ENSC 483 HW#2 SolutionM. Saif 1 Simon Fraser University School of Engineering Science ENSC 483 - Modern Control Systems 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 rep- resented 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. Solution: (a) Note that [ v 1 v 2 ] = [ v 3 v 4 ] T where T is a nonsingular 2 2 matrix that relates the two basis. Verify now that in this case: T = 4 9 2 1 2- 1 2 1 (b) Note that v = [ v 1 v 2 ] where is the representation of v with respect to B 1 basis. You can easily calculate it to be = 1- 1 (c) Based on the result in part (a), we can find the representation of v with respect to the B 2 basis as = T = 4 9 2 1 2- 1 2 1 1- 1 = 2 3 1- 1 (d) To verify (c) simply try to directly find the representation of v with respect to B 2 : v = [ v 3 v 4 ] where is the representation of v with respect to B 2 basis. = 2 3 1- 1 which agrees with the result in (c). ENSC 483 HW#2 SolutionM. Saif 2 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 ( < 4 , < ): y 1 = 1 3- 1 ; y 2 =...
View Full Document

Page1 / 6

e483h2s_07 - ENSC 483 HW#2 SolutionM. Saif 1 Simon Fraser...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online