Matrix Solutions to Systems of Linear Equations

Matrices are the most common and effective way to solve systems of linear equations. However, not all systems of linear equations have unique solutions. Before spending time trying to solve a system, it is important to establish whether it in fact has a unique solution.

For this Discussion Board, 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.

Additional Information for this assignment
 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.

 Discuss what are consistent and inconsistent systems
 Create your own example of an inconsistent system of equations
 Write these equations
 Provide the augmented matrix for your equations
 Show the row operations. I suggest you work with 2 variables and keep it simple
 State your conclusion
 Provide graphs of your equations

 An inconsistent example is
2x + y = 5
4x+2y = 8

 An consistent example with many solutions is
2x + y = 4
-6x - 3y = -12

 A trick is to create your own equation, then double your first equation to get a second new equation