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Determine all possibilities for the solution set of a homogeneous system of 6 equations in 5 unknowns.(a) only one(b) zero(c) one or infinitely many(d) finitely manyThe question was posed to me in an interview for job.This is a very interesting question from Counting in section Counting of Discrete Mathematics

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The correct ANSWER is (c) one or infinitely many

Best explanation: SINCE the system is homogeneous and there are more EQUATIONS than the number of unknowns, so the possibilities are either a UNIQUE solution or infinitely many SOLUTIONS. However, if the rank r of the system is 5, then it can be a unique solution as well as if r<5, then there are infinitely many solutions.



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