Solution Set Visualizer

Run the Solution Set MicroSim Fullscreen

Edit the MicroSim with the p5.js editor

About This MicroSim

This visualization helps you understand the three possible outcomes when solving a system of linear equations:

1. Unique Solution: Exactly one answer exists
2. Infinite Solutions: A line, plane, or higher-dimensional subspace of answers
3. No Solution: The system is inconsistent

Solution Types Explained

Type	RREF Indicator	Geometric Meaning
Unique	All variable columns are pivot columns	Lines/planes meet at exactly one point
Infinite	Some columns are not pivot columns (free variables)	Lines/planes overlap along a line or plane
None	Row of form [0 0 ... 0 | c] where c ≠ 0	Lines/planes are parallel, never meeting

Variables Classification

Basic Variables (pivot columns - highlighted yellow):

• Correspond to pivot columns in RREF
• Their values are determined by the free variables
• Appear in the parametric solution

Free Variables (non-pivot columns - highlighted blue):

• Correspond to non-pivot columns
• Can take any real value
• The number of free variables equals the dimension of the solution set

Lesson Plan

Learning Objectives

After using this MicroSim, students will be able to:

1. Classify systems as having unique, infinite, or no solutions
2. Identify basic and free variables from the RREF
3. Understand the geometric meaning of each solution type
4. Connect the algebraic analysis to geometric visualization

Suggested Activities

1. Explore Each Type: Select each preset and observe how the RREF reveals the solution type
2. Count Free Variables: For infinite solutions, count the free variables and relate to the solution geometry
3. Find Inconsistency: For the "No Solution" case, identify the inconsistent row
4. Predict Before Viewing: Before checking RREF, predict the solution type from the original matrix