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Provide an Example of a Matrix that Has No Solution

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Provide an example of a matrix that has no solution. Use row operations to show why it has no unique solution. Also, some matrices have more than one solution (in fact, an infinite number of solutions) because the system is undetermined. (In other words, there are not enough constraints to provide a unique solution.) Provide an example of such a matrix, and show, using row operations, why it is underdetermined.

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Solution Summary

Matrices with no solutions and infinite solutions: a step-by-step example of each.

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Hi, and welcome!

A matrix with no solution:

4 10 6
4 10 5

(based on the equations: 4x + 10y = 6 and 4x + 10y = 5)

Use a row operation: R2 = R1-R2

4 10 6
0 0 5

The second row of this ...

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