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Unformatted text preview: ECE 301, Homework #6, due date: 10/05/2011 http://cobweb.ecn.purdue.edu/ ∼ chihw/11ECE301F/11ECE301F.html Question 1: [Basic] 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 when x 1 , x 2 , and x 3 being orthonor mal . Please refer to any linear algebra textbook or website, or come to the office hours if you are not familiar with that formula. It might take too much time for you to rederiveyou are not familiar with that formula....
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 Fall '06
 V."Ragu"Balakrishnan
 Fourier Series, Fourier series representation, Fourier series coefficients

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