Finding the amount of solutions in a 3 equation solution x + 2 y +...
Finding the amount of solutions in a 3 equation solution
Answer & Explanation
We have the system
The associated augmented coefficient matrix is given by:
Use Gaussian Elimination (row reduction using elementary row operations). If you encounter a row with all zeros, then you'll know there are infinitely many solutions. You'll have an inconsistent system, for which there are NO solutions, if you obtain a row such as
where . Otherwise, the system will have one unique solution.
If you row reduce correctly, you should obtain a reduced row form as follows:
Infinite amount of solutions