Solution Set of a Linear System
Explore how to determine if a linear system has no solution, a unique solution, or infinitely many solutions by analyzing the reduced row echelon form. Understand pivot and free variables, and apply these concepts using Python code to interpret solution sets effectively.
Given a system of linear equations, there are two questions we can ask about its solution:
- Does a solution exist?
- If a solution exists, is it unique?
Solution set of a linear system and
Because the reduced row echelon form () is the maximally simplified version of a linear system, it’s easier to comprehend the solution from the than from the original system. The two questions stated above can be answered by a simple analysis of of a linear system. However, to perform that analysis, we need to be familiar with a few simple terminologies.