Playground & Quiz

Free exploration with 2D and 3D sandboxes. Test your understanding with comprehensive quiz questions.

Playground & Quiz

Now it's your turn! Use the sandboxes to experiment freely with any matrix you can imagine. Then test your understanding with the quiz.

Try building your own transformations, observe how determinants and eigenvalues change, and discover patterns on your own.

2D Sandbox

Edit the 2×2 matrix directly or use presets. Watch the grid transform, see the basis vectors move, and observe eigenvector directions.

Matrix A
Determinant:1.000
λ₁:1.00
λ₂:1.00

3D Sandbox

Explore 3×3 matrices in three dimensions. Drag to rotate the view, and watch how the unit cube transforms under different matrices.

3×3 Matrix
Determinant:1.000
Orientation preserved
Drag to rotate view • Scroll to zoom
î = X-axis
ĵ = Y-axis
k̂ = Z-axis

Test Your Knowledge

25 questions covering vectors, transformations, composition, determinants, and eigenvectors. Filter by topic or try them all!

Question 1 of 25Score: 0/0
Vectors

What is the result of adding vectors (2, 3) and (1, -1)?

You've Completed the Linear Algebra Module!

Congratulations! You now have an intuitive understanding of linear algebra's core concepts.

  • Vectors can be added and scaled to reach any point in their span
  • Matrices are just a way to describe where basis vectors land
  • Composition is matrix multiplication—order matters!
  • Determinants measure how area/volume scales (and if orientation flips)
  • Eigenvectors are the special directions that only stretch

These ideas appear everywhere: computer graphics, physics, machine learning, quantum mechanics, and much more. Keep exploring!