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A scientist solves a nonhomogencous System of 10 linear equations in 12 unknowns and finds that three of the unknowns are free variables. Can the scientist be certain that, if the right sides of the equations are changed, the new homogencous system will have a solution ? To get the answer for above question, answer the followings (a) What is the order of the coefficient matrix? (b) ColA is a subspace of the vector space (c) What is dim Nul A ? (d) Write down the rank theorem. (e) What is rank A ? (f) What is dimCoIA ? (g) What is the conclusion for scientist's problem.

Practical Management Science

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter11: Simulation Models

Section: Chapter Questions

Problem 54P

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A scientist solves a nonhomogencous System of 10 linear equations in 12 unknowns and finds that three of the unknowns are free variables. Can the scientist be certain that, if the right sides of the equations are changed, the new homogencous system will have a solution ? To get the answer for above question, answer the followings (a) What is the order of the coefficient matrix? (b) ColA is a subspace of the vector space (c) What is dim Nul A ? (d) Write down the rank theorem. (e) What is rank A ? (f) What is dimCoIA ? (g) What is the conclusion for scientist's problem.

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