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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? 

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?  Correct Answer Only III is true

Statement I:

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

Let us suppose m = 2, n = 3

x + 2y + z = 3

x + y + z = 3

here, this will not give any solution. Because, when we have 2 equations with 3 variables, we can’t find the solution for this.

Statement II:

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

Consider, m = 3, n = 2

System of equation will be like:

x + 2y = 2

x + y = 1

2x + 5y = 3

But here we can easily find the value of x and y.

Statement III:

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

Consider m = 2, n = 2

System of equation will be like:

x + 2y = 3

2x + 4y = 4

Here, x and y can be calculated. These systems of equations have a solution.

Related Questions

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