Unformatted text preview: v (1) = [1 1 1 ] T , v (2) = [ 21 3 ] T , and s = [ 1 2 3 ] T . (i) Determine the projection ˆ s of s on the plane deﬁned by v (1) and v (2) . (ii) Show that the projection of ˆ s on v (1) is the same as the projection of s on v (1) . (Is this result expected from threedimensional geometry?) S 15.2 ( P 2.26 in textbook). Let a (1) , a (2) , a (3) and a (4) be the columns of the matrix A = 1 1 / 2 1 / 4 1 / 8 1 1 / 2 1 / 4 1 1 / 2 1 Determine the least squares approximation p = c 1 a (1) + c 2 a (2) + c 3 a (3) of a (4) based on a (1) , a (2) and a (3) . Also determine the relative (root mean square) error k pa (4) k k a (4) k...
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 Spring '08
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 Linear Algebra, Vector Space, Least Squares, Euclidean space, error vector

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