## MATH10260: Linear Algebra for Engineers     Semester 2, 2015

### Dr Masha Vlasenko

G12 Science North, School of Mathematical Sciences

This is a basic subject on matrix theory and linear algebra. Emphasis is given to topics that will be useful in other disciplines, including systems of equations, vector spaces, determinants, eigenvalues and similarity.

### Assessment

The following grading scheme will be applied to the final mark.

### Syllabus

1. Numbers and polynomials.
2. Systems of linear equations.
3. Eigenvalues and eigenvectors.
• (3.1) Eigenvalues and eigenvectors
• (3.2) The Cayley-Hamilton theorem and diagonalization  /  (part 2)
• (3.3) Trace, determinant and eigenvalues
4. Vector spaces and linear maps.
• (4.1) Linear independence, bases and dimension  /  (part 2) /  (part 3)
• (4.2) Linear maps and matrices
• (4.3) Rank of a matrix and applications to linear systems
• (4.4) Matrix of a linear map. Change of bases and similarity
5. Vectors and three-dimensional geometry.
• (5.1) Lines and planes
• (5.2) Dot product, cross product, and their applications  /  (part 2)

### Literature

Numbers and Polynomials:
• Bernard Kolman, Arnold Shapiro, College Algebra and Trigonometry / shelf 512.03 (in James Joyce Library, top floor)
• Charles C. Carigo, College Algebra and Trigonometry / 512.13
The rest of the course:
• Bernard Kolman, Introductory Linear Algebra with Applications / 512.5
• Gilbert Strang, Linear Algebra and Its Applications / 512.5
 Here are the last year's final [exam paper] and [solutions]. This year's paper layout is different. There will be 8 questions (some of which have parts a,b,c...). Full marks will be given for complete answers to ALL questions. Correctness of the final numerical answer is important for evaluation. Uncollected homeworks can be found in the box located at the ground floor of Sceince North under the staircase. It looks approximately like this -----> Please make sure you leave the box at the same place. Maths Help Centre reports that many students are struggling with determinants. Please note the following: in the final exam there will be no questions like in Problem Set 7. What you really need is to be able to compute determinants, for which the most efficient method is the cofactor expansion.