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# tut5 - U = Span 1 x,x 2 3 Let U and W be subspaces of an...

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Math 235 Tutorial 5 Problems 1: In R 4 let W = Span 1 1 0 1 , 0 1 1 1 , 1 0 - 1 0 . a) Use the Gram-Schmidt procedure to produce an orthogonal basis for W . b) Find the projection of ~x = 2 3 5 6 onto W . c) Find an orthogonal basis for W . 2: In P 2 with inner product < p ( x ) , q ( x ) > = p (0) q (0) + p (1) q (1) + p (2) q (2). Find the projection of f ( x ) = 1 + x 2 onto the subspace
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Unformatted text preview: U = Span { 1 + x,x 2 } . 3: Let U and W be subspaces of an inner product space V . Prove that if U is a subspace of W , then W ⊥ is a subspace of U ⊥ . 4: Let ~v be a vector in an inner product space V and let U be a ﬁnite dimensional subspace of U . Prove that k ~v k ≥ k proj U ~v k . 1...
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