HW5 - ECE 301, Homework #5, due date: 2/17/2010...

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Unformatted text preview: ECE 301, Homework #5, due date: 2/17/2010 http://cobweb.ecn.purdue.edu/ ∼ chihw/10ECE301S/10ECE301S.html Question 1: Review of linear algebra: Consider row vectors of dimension 3. Let x 1 = ( √ 2 / 2 ,- √ 2 / 2 , 0), x 2 = ( √ 3 / 3 , √ 3 / 3 , √ 3 / 3), and x 3 = ( √ 6 / 6 , √ 6 / 6 ,- 2 √ 6 / 6)) • Show that { x 1 ,x 2 ,x 3 } is an orthonormal basis. Namely, show that | x i | 2 = 1 for all i = 1 , 2 , 3, and show that the inner product x i · x j = 0 for i 6 = j . • If we know that x = 0 . 7 x 1 + 0 . 3 x 2 + 0 . 4 x 3 , find x . • If we know that x = (0 . 7 , . 3 , . 4), find α 1 , α 2 , α 3 such that x = α 1 x 1 + α 2 x 2 + α 3 x 3 . • Why are we interested in rewriting x = α 1 x 1 + α 2 x 2 + α 3 x 3 ? Note: There is a simple formula of solving α 1 , α 2 , α 3 as x 1 , x 2 , and x 3 being orthonormal . Please refer to any linear algebra textbook or website, or come to my office hours if you are not familiar with the formula. It might take too much time for you to re-derive existingnot familiar with the formula....
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This note was uploaded on 02/22/2010 for the course ECE 301 taught by Professor V."ragu"balakrishnan during the Spring '06 term at Purdue University.

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HW5 - ECE 301, Homework #5, due date: 2/17/2010...

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