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# tanotes2 - CO 350 Linear Optimization TAs comments for...

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CO 350 Linear Optimization TA’s 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 = 0 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 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 is x 1 = 0. So

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tanotes2 - CO 350 Linear Optimization TAs comments for...

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