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Determine all possibilities for the solution set of a homogeneous system that has y1 = 5, y2 = −3, y3 = 2 as a solution.(a) one(b) finitely many(c) infinitely many(d) either one or infinitely manyThis question was posed to me in an online quiz.I'd like to ask this question from Counting topic in portion Counting of Discrete Mathematics

Answer»

The CORRECT option is (c) infinitely MANY

Explanation: The possibilities for the solution SET for any homogeneous system is either a unique solution or infinitely many solutions. Since the homogeneous system has the zero solution and y1 = 5, y2 = −3, Y3 = 2 is another solution, it has at least two distinct solution. Thus the only possibility is infinitely many solutions.



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