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
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.