Course - Linear Algebra and Geometry - MA6201
MA6201 - Linear Algebra and Geometry
About
Examination arrangement
Examination arrangement: School exam
Grade: Letter grades
| Evaluation | Weighting | Duration | Grade deviation | Examination aids |
|---|---|---|---|---|
| School exam | 100/100 | 4 hours | D |
Course content
This course is equivalent to MA1201, adapted to further education. 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.
Learning outcome
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
Exercises and final written exam. Physical or digital gatherings (agreed upon at the start of the semester with the students). Parts of this course can be taught in English.
Compulsory assignments
- Exercises
Further on evaluation
The re-sit examination may be given as an oral examination. The retake exam is in August.
Specific conditions
Admission to a programme of study is required:
- (KDELTA)
Recommended previous knowledge
The course is based on Mathematics R2 from high school, or equivalent.
Course materials
Will be announced at the start of the course.
Credit reductions
| Course code | Reduction | From | To |
|---|---|---|---|
| MA1201 | 7.5 | ||
| MA0003 | 1.5 | AUTUMN 2009 | |
| TMA4110 | 3.0 | AUTUMN 2012 | |
| TMA4115 | 3.0 | AUTUMN 2012 | |
| TMA4101 | 3.7 | AUTUMN 2020 | |
| TMA4106 | 3.7 | AUTUMN 2020 |
Version: 1
Credits:
7.5 SP
Study level: Further education, lower degree level
Term no.: 1
Teaching semester: AUTUMN 2024
Language of instruction: Norwegian
Location: Trondheim
- Mathematics
Department with academic responsibility
Department of Mathematical Sciences
Department with administrative responsibility
Section for quality in education and learning environment
Examination
Examination arrangement: School exam
- Term Status code Evaluation Weighting Examination aids Date Time Examination system Room *
- Autumn ORD School exam 100/100 D INSPERA
-
Room Building Number of candidates - Summer UTS School exam 100/100 D INSPERA
-
Room Building Number of candidates
- * 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"