GATE | GATE-CS-2016 (Set 2) | Question 14

Consider the systems, each consisting of m linear equations in n variables.

I. If m < n, then all such systems have a solution
II. If m > n, then none of these systems has a solution
III. If m = n, then there exists a system which has a solution

Which one of the following is CORRECT?
(A) I, II and III are true
(B) Only II and III are true
(C) Only III is true
(D) None of them is true


Answer: (C)

Explanation:  

For ‘n’ variables, we need atleast ‘n’ linear equations in terms of the given  variable to find value of each variable. If no. of equations > no. of variables then also we can find the value of each variable.
Here, m : No. of linear equations
n : No. of variables For solution, m > or = n.



This solution is contributed by Mohit Gupta.


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