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Linear Algebra
Vectors and the matrices that move them. Every operation is shown row by row, and 2×2 and 3×3 matrices are drawn in 3D so you can see what a determinant or an eigenvector actually is.
Lessons
Core
Determinants
2×2 by ad − bc, larger by cofactor expansion — and what the number means.
det [[1,2],[3,4]]
Core
Matrix inverse
The 2×2 formula and Gauss–Jordan elimination for the rest.
inverse of [[1,2],[3,4]]
Advanced
Eigenvalues and eigenvectors
The characteristic polynomial and the directions a matrix only stretches.
eigenvalues of [[2,1],[1,2]]
Introductory
Matrix multiplication
Rows times columns, entry by entry.
[[1,2],[3,4]] * [[5,6],[7,8]]
Core
Row reduction
Gaussian elimination, rank and solving Ax = b.
rref [[1,2,3],[4,5,6],[7,8,9]]
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