❖ A linear system Ax=b has one of three possible solutions:

1. The system has a unique solution which means only one solution.
2. The system has no solution.
3. The system has infinitely many solutions.

So, we have explained how to determine if a system of equations has the three types of solution which are a unique solution, no solution, or infinitely many solutions. Also, this algebra video tutorial explains how to solve systems of equations by elimination with examples and practice problems.

❖ In this video, the three augmented matrices represent the final step for any augmented matrix by using a Gauss Jordan Elimination method.

The Gauss Jordan elimination method is a process used to solve a system of linear equations Ax=b by converting the system into an augmented matrix and using Elementary Row Operations to convert a matrix into a Reduced Row Echelon Form ( RREF ).

Another method to solve a linear system Ax=b is a Gaussian elimination method.

❖ Elementary Row Operations

There are three types of elementary matrices, which correspond to three types of row operations:

1. Row switching
   A row within the matrix can be switched with another row.
2. Row multiplication
   Each element in a row can be multiplied by a non-zero constant.
3. Row addition
   A row can be replaced by the sum of that row and a multiple of another row.