• Preface; Part I: 1. Gaussian elimination; 2. Solutions to simultaneous equations I; 3. Matrices and algebraic vectors; 4. Special matrices; 5. Matrix inverses; 6. Linear independence and rank; 7. Determinants; 8. Solutions to simultaneous equations II; 9. Vectors in geometry; 10. Straight lines and planes; 11. Cross product; Part II: 12. Basic ideas; 13. Subspaces of Rn; 14. Spanning lists, bases, dimension; 15. Rank; 16. Linear transformations; 17. Change of basis; 18. Eigenvalues and eigenvectors; 19. Diagonalisation I; 20. The dot product; 21. Orthogonality; 22. Diagonalisation II; 23. Geometry; 24. Differential equations; Answers to exercises; Sample test paper for part I; Sample test paper for part II; Index.

'The book is clearly directed at students who have had little or no experience of solving linear equations at school. Moreover, it is intended for people who do not find learning mathematics easy. There are no short cuts, or bribes in the form of interesting applications, but the student who is motivated to learn about systems of linear equations, and willing to work through the exercises, will have an excellent opportunity to acquire proficiency and understanding.' The Times Higher Education Supplement