How to tell if a matrix is consistent?
Understand the Problem
The question is asking for the criteria or methods to determine whether a matrix is consistent, which refers to the existence of solutions to a system of equations represented by the matrix.
Answer
Check if the ranks of the coefficient matrix and augmented matrix are equal.
The final answer is to check if the ranks of the coefficient matrix and the augmented matrix are equal. If they are equal, the matrix is consistent.
Answer for screen readers
The final answer is to check if the ranks of the coefficient matrix and the augmented matrix are equal. If they are equal, the matrix is consistent.
More Information
The concept of matrix consistency is important in understanding solutions to linear systems. By using this method, one can determine whether the system has at least one solution.
Tips
A common mistake is not transforming the matrix into Row Reduced Echelon Form (RREF) before comparing the ranks.
Sources
- Consistent and Inconsistent Equations - Wikipedia - en.wikipedia.org
- Determining if a System of Equations is Consistent - Mathwizurd - mathwizurd.com
- Distinguishing between consistent and inconsistent system of equations based on rank of matrices - ma.mathforcollege.com
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