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Determine all possibilities for the solution set of a homogeneous system of 6 equations in 5 unknowns.

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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 many

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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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