University of Twente
Linear Algebra
Built from the course syllabus and past papers. Upload your lecture notes to tune it further to your lecturer.
1Systems of Linear Equations
Solving systems of linear equations using Gaussian elimination · 7 steps
FREE2Matrix Algebra and Invertibility
Matrix operations and computing matrix inverses · 7 steps
FREE3Determinants
Computing and interpreting determinants · 7 steps
4Vector Spaces and Subspaces
Vector spaces and subspaces · 7 steps
5Basis and Dimension
Basis, dimension, and rank of vector spaces · 7 steps
6Linear Transformations
Linear transformations and their matrix representations · 7 steps
7Eigenvalues and Eigenvectors
Computing eigenvalues and eigenvectors · 7 steps
8Diagonalization
Diagonalizing matrices using eigenbasis · 7 steps
9Inner Product Spaces and Orthogonality
Inner products, orthogonality, and orthonormal bases · 7 steps
10Orthogonal Projections and Least Squares
Orthogonal projections and least squares approximation · 7 steps
11Symmetric Matrices and Orthogonal Diagonalization
Spectral theorem for symmetric matrices · 7 steps
12Exam Practice and Integration
Integrated review of linear algebra techniques through past exam problems · 7 steps
Practice
Mixed retrieval practice across everything you've been taught, weighted to the topics worth the most marks and scheduled so it comes back before you forget.
Opens after 2 more lessons
Mock exam
The real paper structure, timed, marked to this course's own scheme — with your marks, your pacing per exercise, and where the marks went.
Exercise 1 free to sit