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Unformatted text preview: affine subspace .] a) Consider the following polyhedron P: {x ∈ R 2  3 x 1 + 2 x 2 = 4} Prove that P is an affine subspace by identifying a subspace S and a vector b such that for any vector x in S , the vector (x + b ) is in P. b) Is your choice of b unique? If yes, prove it. If no, define the set of all valid vectors b . c) Consider the following polyhedron P: {x ∈ R n  Ax = b} where A is an mxn matrix and b is a column vector in R m . Prove that P is an affine subspace by identifying a subspace S and the set of vectors {b }such that for any vector x in S , the vector (x + b ) is in P. d) For what matrices A will there only be one valid vector b ?...
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 Fall '08
 STAFF
 Linear Algebra, Vectors, Row vector, Bertsimas

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