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Unformatted text preview: CO 350 Linear Optimization TAs comments for Assignment 2 General: It seems many students are confused about basic operations in linear algebra. Below we list some examples of mistakes of these types. Watch out for them. (i) If A is a matrix and Ax = 0 for some vector x 6 = 0, then A = 0. This is false: take A = 1 0 and x = 1 . (ii) If x 0 is not zero, then x is positive. First of all, you would need to define what it means for a vector to be positive. If you consider that x is positive is the same as x i > 0 for every i , then this is false: take x = (0 , 1) t . (iii) If x,y are vectors with x t y > 0, then x and y are positive. This has the same problem of defining positive as before, but this time the statement fails already for real numbers: ( 1) ( 1) = 1 > 0. There is also a lot of confusion about the term unbounded LP. Consider the following example (an LP with two variables): minimize x 1 subject to x 1 = 0 x 2 = 0 Note that the feasible solutions for this LP are all points in R 2 of the form (0 ,x 2 ), where x 2 is any real number. Thus, the objective value of each feasible point isnumber....
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This note was uploaded on 05/28/2011 for the course CO 350 taught by Professor S.furino,b.guenin during the Winter '07 term at Waterloo.
 Winter '07
 S.Furino,B.Guenin

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