Unformatted text preview: 21 6 1 31 2 ∼ 21 6 2 91 2 ∼ 21 6 131 2 (2) For any matrix M , the rank of the row vectors is equal of the rank of the column vectors. Hence, if M has only 3 rows there are at most 3 linearly independent columns. Ex 3. (1) For any feasible solution [ x 1 x 2 x 3 ] T ,x 1 + x 2 ≤ x 1 + 2 x 2 = ( x 1 + x 2 + x 3 )(2 x 1x 2 + x 3 ) ≤ where the ﬁrst inequality follows from the fact that x 2 ≥ and the second one from the fact that x 1 + x 2 + x 3 ≤ 1 and that 2 x 1x 2 + x 3 = 1 . (2) The vector [0 0 1] T is a feasible solution with objective value . It follows from part (1) that it is an optimal solution. 1...
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 Winter '07
 S.Furino,B.Guenin
 Linear Algebra, optimal solution, feasible region

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