PSET 2 SOL - MS&E 111 Introduction to Optimization...

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Elementary Linear Algebra
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Chapter 5 / Exercise 10
Elementary Linear Algebra
Larson
Expert Verified
MS&E 111: Introduction to OptimizationInstructor: Professor Amin Saberi ([email protected])HW#2 – Due Thursday, April 24thHomework drop-o:you should deposit your homework in MS&E 111 drop-obox locatedin Huang basement before 12:30 pm on the due date.We do not collect any homework in class.1. (Linear Algebra)a=26666414-123377775, b=266664120-31377775, c=26666402-152377775, d=266664101-8-1377775, e=266664110-1179377775, f=266664-4-21.5272377775(a) The span ofa, b, cis anNdimensional subspace ofRM. What areMandN?(b) What is 6a+ 5b-3e+ 2f?(c) The span ofa, b, c, d, e, fis anNdimensional subspace ofRM. What areMandN?Solution:(a)a, b, care vectors with 5 components, hence they belong toR5
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Elementary Linear Algebra
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Chapter 5 / Exercise 10
Elementary Linear Algebra
Larson
Expert Verified
2. (Graphical Method) Consider the region described by the constraints below and answerthe questions that follow.x10x202x1+x211-x1+x23x14x25(a) Plot the feasible region described by the above constraints and identify its extremepoints.2
(b) What value(s) of (x1, x2) maximizes the functionf(x1, x2) =x1+ 2x2?Whatvalue(s) of (x1, x2) minimizes the functionf(x1, x2)?Solution:
3

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