Course - Linear Algebra and Geometry - MA1201
MA1201 - Linear Algebra and Geometry
The course takes up basics of logic and set theory, methods of proof, and complex numbers. We solve linear equations using Gaussian elimination, and learn to write equations with vectors and matrices, and to interpret row operations as multiplication with elementary matrices. We discuss matrix calculus in general, including finding the inverse of a matrix arithmetic rules inverses, transposed, and the like. Geometrically we begin studying properties of vectors in the plane and space (including dot product, cross product). From there, we develop the concepts of subspaces, basis, dimension, and abstract vector spaces. Special emphasis is placed on the vector spaces attached a matrix (null space, column space, row space) and the rank-nullity theorem. We consider linear maps, both geometrically and algebraically, and show how the matrices describing a linear map changes when changing the bases. Determinants are introduced, both as a criterion for when matrices are invertible, and in dimension 2 and 3 as area and volume. We show Cramer's rule. Eigenvalues and vectors are introduced. It is proven that a matrix is diagonalisable if and only if there exists a basis consisting of eigenvectors. We show that real symmetric matrices always are orthogonally diagonalizable, and uses this in the principal axis transformation to investigate / classify conic sections.
1. Knowledge. The student knows the basic concepts and methods in linear algebra, including vector spaces, subspaces, basis, dimension. Moreover, students know linear maps, both algebraically / in matrix form (including solution of linear systems of equations) and geometrically (including eigenvalues and eigenvectors). 2. Skills. The student is able to recognize linear problems and formulate them using linear equations and solve them using matrices and Gaussian elimination. The student is able to work with linear maps using matrices, including on geometric problems. In particular, the student is able to study conic sections using principal axis transformations. The student is able to give elementary mathematical proofs and do calculations using complex numbers.
Learning methods and activities
Lectures, compulsory exercises and mid-semester examination. Portfolio assessment is the basis for the grade awarded in the course. This portfolio comprises a written final examination (80%) and the mid-semester examination (20%). The mid-semester examination only counts if it has a positive effect on the final grade. The results for the constituent parts are to be given in %-points, while the grade for the whole portfolio (course grade) is given by the letter grading system. The re-sit examination may be given as an oral examination.
Further on evaluation
For more information about grading and evaluation, see «Teaching methods and activities».
Compulsory activities from previous semester may be approved by the department.
Recommended previous knowledge
The course is based on Mathematics R2 or 3MX from high school or equivalent.
Will be announced at the start of the course.
Credits: 7.5 SP
Study level: Foundation courses, level I
Term no.: 1
Teaching semester: AUTUMN 2021
Language of instruction: -
Examination arrangement: Portfolio assessment
- Term Status code Evaluation Weighting Examination aids Date Time Examination system Room *
- Autumn ORD Semester test 20/100 A 2021-10-05 12:00
Room Building Number of candidates SL274 Sluppenvegen 14 8 SL410 blå sone Sluppenvegen 14 35 SL311 lyseblå sone Sluppenvegen 14 96 SL311 brun sone Sluppenvegen 14 81 SL410 orange sone Sluppenvegen 14 42
- Autumn ORD School exam 80/100 D 2021-12-06 09:00
Room Building Number of candidates Storhall del 1 Idrettssenteret (Dragvoll) 204 SL274 Sluppenvegen 14 6 DI42 Idrettssenteret (Dragvoll) 7 DI172 Idrettssenteret (Dragvoll) 4
- * The location (room) for a written examination is published 3 days before examination date. If more than one room is listed, you will find your room at Studentweb.
For more information regarding registration for examination and examination procedures, see "Innsida - Exams"