Question: (7.3 #4) Consider the matrix 1 1 0 0 A: D D 2 2 . 1 1 1 1 (a) Compute the best tting line

(7.3 #4) Consider the matrix 1 1 0 0 A: D D 2 2 .
(7.3 #4) Consider the matrix 1 1 0 0 A: D D 2 2 . 1 1 1 1 (a) Compute the best tting line L and best tting plane P to the four columns of A. Express L and P as the span of vectors. (b) Compute the rank one decomposition of A, and the approximations A1 and A2. (c) Check that the columns of A1 are the projections of the columns of A on L. ((1) Check that the third column of A2 is the projection of the third column of A on P. (e) Compute the 2norm of A A1. (f) Construct a rank one matrix B of your choice and the same size as A. Check that B is not closer to A than A1

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