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Unformatted text preview: p = V*c = c1*v1 + c2*v2 + c3*v3 = [ 11/3 5/3 4 8/3 ].' (iv) The error vector is ps = [ 2/3 2/3 0 4/3 ].' and its norm equals ps = 1.6330 (v) v4 = [ 14 2 0 8 ].' V = [v1 v2 v3 v4] V = [ 5 5 1 14 3 1 1 2 1 7 10 0 1 3 0 8 ] V is nonsingular. Therefore, the range of the matrix V is R^4 which represents the set of all points in the 4dimensional space. It can also show that any point x = [x1 x2 x3 x4].' can be uniquely represented in terms of a linear combination of columns of V. This includes x=s, and thus the projection of s on the range of the matrix V is s itself. The resulting error norm is zero. ( Note that s = v4  v1  v2  v3 , i.e., s = V * [1 1 1 1].' )...
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 Spring '08
 staff
 Linear Algebra, Vector Space, v1 v2, error vector

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