Linear Algebra

10 units · licensed

Matrices as maps: solving systems, determinants and inverses, vector spaces, eigenvalues and least squares.

Unit 1

Systems and row reduction

Elimination, echelon form and the shape of a solution set

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Unit 2

Matrix algebra

Products, powers, transposes and the trace

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Unit 3

Determinants

Cofactor expansion, row operations and singular matrices

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Unit 4

Inverses and Ax = b

Adjugates, Cramer's rule and what invertibility is equivalent to

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Unit 5

Vector spaces and independence

Span, bases, coordinates and subspaces of Rⁿ

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Unit 6

Rank and the four subspaces

Rank and nullity, free variables and column spaces

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Unit 7

Linear transformations

Standard matrices, compositions, images and preimages

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Unit 8

Eigenvalues and eigenvectors

Characteristic polynomials, eigenvectors and what they fix

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Unit 9

Orthogonality and least squares

Projections, unit vectors, normal equations and fitting a line

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Unit 10

Diagonalisation

Writing A as PDP⁻¹, powers of a matrix, and when it is possible

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Loop practice

Cycle through all 10 units until you get 200 right (20 × 10 units).

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