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Unformatted text preview: , 1) T , (1 , , 1 , 2) T ), A = 11 1 1 1 1 2 , b = 2 4 . (a) Find bases for S and S . (b) Solve the normal equations A T A x = A T b . (c) Find the orthogonal projection p of b onto S (ie. nd the vector p S such that bp S ). (d) Find min s S  bs  ; ie. nd the minimum of  bs  for s S and b = (0 , 2 , , 4) T . 5. (10 points) Let U and V be subspaces of a vector space W . (a) Dene what it means to say that W is the direct sum of U and V . (b) Prove that if W = U V then U V = { } . 1...
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This note was uploaded on 12/27/2011 for the course MAS 4105 taught by Professor Rudyak during the Spring '09 term at University of Florida.
 Spring '09
 RUDYAK

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