A unique solution, No solution, or Infinitely many solutions | Ax=b
❖ 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.
0:00 ❖ Types of solution of Ax=b
7:30 1. a unique solution (only one solution)
9:25 2. no solution
10:50 3. infinitely many solutions
For more videos about this, you can find them in this playlist (Linear Algebra):
• Linear Algebra
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