Question

Consider the systems, each consisting of $m$ linear equations in $n$ variables
1.If $m<n$ , then all such systems have a solution.
2.If $m>n$, then none of these systems has a solution.
3.If $m=n$ , then none of these systems has a solution.
Which one of the following is CORRECT?

• A. 1,2 and 3 are true
• B. only 2 and 3 are true
• C. only 3 is true
• D. none of them is true

Answer 1

The correct option is C only 3 is true

Statement-1 is not correct because under determined system may have no solution.
Statement-2 is not correct because over determined system can also have unique solution or infinite solution.
Statement-3 is correct because equally determined system have all three possibilities i.e. may have unique solution. or infinite solution or no solution.