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# tut5 - U = span 1 x,x 2 3 In M(2 2 let W = span ±² 1 0 0...

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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: In M (2 , 2), let W = span ±² 1 0 0 1 ³ , ² 0 1 1 0 ³´ . Find an orthogonal basis for the orthog-onal complement of W under the inner product h A,B i = tr( B T A ). 4: Find a and b to obtain the best ﬁtting equation of the form y = a + bx 2 for the given data. x-1 1 3 y 1 0 5 . 1...
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