Unformatted text preview: 2 ,..., ~Î± k } be a set of mutually orthogonal vectors in R n . 1. Show that for any ~v âˆˆ R n , the vector ~v(proj ~Î± 1 ( ~v ) + proj ~Î± 2 ( ~v ) + Â·Â·Â· + proj ~Î± k ( ~v )) is orthogonal to each of the ~Î± 1 , ~Î± 2 ,..., ~Î± k . 2. Verify this claim for R 3 with ~ Î± 1 = ~ e 1 , ~ Î± 2 = ~ e 2 , and letting ~v = 1 2 3 . Draw a picture. 1...
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 Spring '05
 CONSANI
 Linear Algebra, Algebra, mutually orthogonal vectors

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