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Determine all possibilities for the solution set of a homogeneous system of 5 equations in 4 unknowns and the rank of the system is 3.(a) finite(b) zero or finitely many(c) only one(d) infiniteThis question was posed to me during an online exam.This is a very interesting question from Counting topic in portion Counting of Discrete Mathematics

Answer»

Right option is (d) infinite

Best explanation: A homogeneous system is consistent. The rank is R = 3 and the number of variables is n = 4. Hence there is n – r = 1 FREE variable. THUS there are infinitely many solutions.



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