Interactive Demo
Linear Combinations & Span Explorer
Linear Combinations & Span Explorer is a free, interactive learning demo from the Spring 2026 - Math 354 - Sections 02/04 course on Lykke. It helps you build intuition for Reduced Row Echelon Form (RREF), Matrix Inversion, Linear Independence, Linear Combinations. Play with it directly in your browser — it features 3 sliders, 1 toggle, direct drag interaction and a live visual canvas. Adjust scalars to see how the linear combination moves. This demo lives in the “Linear Algebra Review and Matrix Operations” section of the course.
How to use this demo
- Adjust scalars to see how the linear combination moves.
- Drag the sliders to change the inputs and watch the visualization update in real time.
- Click and drag directly on the canvas to manipulate the scene.
- Toggle the checkboxes to show or hide layers and compare cases.
- Experiment freely — there's nothing to break, and every change is reversible.
What you'll explore
- Reduced Row Echelon Form (RREF)
- Matrix Inversion
- Linear Independence
- Linear Combinations
- Vector Spaces
Frequently asked questions
What does the Linear Combinations & Span Explorer demo do?
A foundational review of linear algebra techniques essential for optimization, focusing on matrix inversion and vector space properties. Linear Combinations & Span Explorer turns that idea into something you can manipulate directly and watch respond.
What Spring 2026 - Math 354 - Sections 02/04 concept does Linear Combinations & Span Explorer teach?
A foundational review of linear algebra techniques essential for optimization, focusing on matrix inversion and vector space properties. It focuses on Reduced Row Echelon Form (RREF), Matrix Inversion, Linear Independence, Linear Combinations, Vector Spaces from the “Linear Algebra Review and Matrix Operations” section.
What can I control in Linear Combinations & Span Explorer?
The sliders change the key inputs; you can drag elements directly on the canvas; toggles show or hide layers so you can compare cases. Every change updates the visualization in real time, so you can see exactly how each variable affects the outcome.
How does Linear Combinations & Span Explorer fit into the Spring 2026 - Math 354 - Sections 02/04 course?
Math 354: Linear Optimization provides a comprehensive introduction to the mathematical theory and application of linear programming. The course covers the transition from foundational linear algebra concepts, such as m… This demo is the interactive piece for the “Linear Algebra Review and Matrix Operations” section. Open the full Spring 2026 - Math 354 - Sections 02/04 course wiki at https://www.getlykke.com/explore/public/spring-2026-math-354-765743ab-3e83-4eb5-ac72-d0dd4db82581 for notes, flashcards, quizzes and the other demos.
What will I understand better after using Linear Combinations & Span Explorer?
You'll build intuition for Reduced Row Echelon Form (RREF), Matrix Inversion, Linear Independence, Linear Combinations, Vector Spaces — and, crucially, see how they behave when you change the inputs, which is hard to get from a textbook or lecture on Spring 2026 - Math 354 - Sections 02/04 alone.
From the Spring 2026 - Math 354 - Sections 02/04 course
This interactive demo is part of the Linear Algebra Review and Matrix Operations section. Explore the full Spring 2026 - Math 354 - Sections 02/04 course wiki on Lykke — with notes, flashcards, quizzes and more interactive demos.
Open the Spring 2026 - Math 354 - Sections 02/04 course →