Unit 1
Matrices and linear systems
Row reduction, inverses and determinants.
Advanced Mathematics · University & competition
Linear Algebra
Vector spaces, matrices, determinants, eigenvalues and diagonalisation.
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What you will be able to do
- Solve linear systems by Gaussian elimination
- Work with vector spaces, bases and dimension
- Compute determinants, eigenvalues and eigenvectors
- Diagonalise matrices and apply them to real problems
Course contents
Every topic, lesson by lesson.
Unit 2
Eigenvalues and eigenvectors
Characteristic polynomials, eigenspaces and diagonalisation.
Unit 3
Eigenvalues and diagonalisation
Characteristic polynomials, eigenvectors and diagonalising matrices.
Unit 4
Inner product spaces
Dot products, orthogonality, projections and Gram–Schmidt.
Concepts to practise again
Built from your saved practice attempts in this course, weakest question types first.
Complete a practice set in any lesson to see which question types to practise again.
Curriculum alignment
This course satisfies the following education systems.
American Curriculum
British Curriculum
Canadian Curriculum
Australian Curriculum