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Unformatted text preview: ~ u 1 and ~ u 2 . This give Proj W ~v = ~v ~ u 1 ~ u 1 ~ u 1 u 1 + ~v ~ u 2 ~ u 2 ~ u 2 u 2 . This is equal to 4 / 11 ~ u 11 / 11 ~ u 2 . Thus the projection vector is b v = 3 / 11 7 / 11 7 / 11 16 / 11 . Let ~ z = ~vb v . Then ~ z is orthogonal to W and is in the span of ~v, ~ u 1 , ~ u 2 . Computing this, we nd 1 ~ z = 8 / 11 4 / 11 4 / 115 / 11 . Note that any nonzero scalar multiple of ~ z will also work. 2...
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 Fall '10
 Russel
 Linear Algebra, Algebra, Addition

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