USTHLinear Algebra · MAT1.002

Modules: slides, worked examples, practice links

Each module has a slide deck in the USTH style (use ← → keys or the buttons; full screen with ⛶), worked examples taken from the course problems, and links to the quizzes and the lab.

Chapter 1 · Systems of linear equations

M1 · Systems of linear equationsLecture 1 · Exercise Sheet 1Augmented matrices, elementary row operations, Gauss and Gauss–Jordan elimination, solution types, systems with a parameter.73 practice questions on this module's topics

Chapter 2 · Matrices

M2 · MatricesLecture 2 · Exercise Sheet 2Operations, the algebra of matrices, transposes, inverses and how to compute them.57 practice questions on this module's topics

Chapter 3 · Determinants

M3 · DeterminantsLecture 3 · Exercise Sheet 3Cofactor expansion, row operations, properties, adjugate and Cramer's rule.40 practice questions on this module's topics

Chapter 4 · Vector spaces

M4 · Vector spacesLecture 4 · Exercise Sheet 4Vector-space axioms, subspaces, span, independence, basis, dimension, rank, coordinates and change of basis.71 practice questions on this module's topics

Chapter 5 · Inner product spaces

M5 · Inner product spacesLecture 5 · Exercise Sheet 5Dot product and inner products, norm, angle, orthogonality, projections, Gram–Schmidt, orthogonal complements, least squares.43 practice questions on this module's topics

Chapter 6 · Linear transformations

M6 · Linear transformationsLecture 6 · Exercise Sheet 6Linear maps, standard matrix, kernel and range, rank–nullity, one-to-one and onto, composition, inverse, matrices relative to bases.76 practice questions on this module's topics

Chapter 7 · Eigenvalues and eigenvectors

M7 · Eigenvalues and eigenvectorsLecture 7 · Exercise Sheet 7Characteristic polynomial, eigenspaces, diagonalization, powers of a matrix, symmetric matrices and orthogonal diagonalization.75 practice questions on this module's topics