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

GATE · 2016 · CS · Set 2 · Computer Science & IT

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

I. If m<nm < n, then all such systems have a solution

II. If m>nm > n, then none of these systems has a solution

III. If m=nm = n, then there exists a system which has a solution

Which one of the following is CORRECT?

  1. A.

    I, II and III are true

  2. B.

    Only II and III are true

  3. C.

    Only III is true

  4. D.

    None of them is true

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