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Determine all possibilities for the number of solutions of the system of 7 equations in 5 unknowns and it has x1 = 0, x2 = −6, and x3 = 4 as a solution.(a) unique or infinitely many(b) unique(c) finitely many(d) zeroI got this question during an internship interview.The question is from Counting topic in section Counting of Discrete Mathematics

Answer» CORRECT answer is (a) UNIQUE or infinitely many

Explanation: Let i be the number of equations and j be the number of unknowns in the given system. Since i> j, the system has at least one SOLUTION x1 = 0, x2 = −6, and x3 = 4 and so it is consistent. Thus, it results in either a unique solution or infinitely many solutions.


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