Question

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) zero

I got this question during an internship interview.

The question is from Counting topic in section Counting of Discrete Mathematics

Answer 1

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.