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MA6201

Linear Algebra and Geometry

Choose study year
Credits 7.5
Level Further education, lower degree level
Course start Autumn 2023
Duration 1 semester
Examination arrangement School exam

About

About the course

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, gatherings and final written exam.

Compulsory assignments

  • Exercises

Further on evaluation

The re-sit examination may be given as an oral examination.

Specific conditions

Admission to a programme of study is required:
KOMPiS Matematikk DELTA (KDELTA)

Course materials

Will be announced at the start of the course.

Credit reductions

Course code Reduction From
MA1201 7.5 sp
MA0003 1.5 sp Autumn 2009
TMA4110 3 sp Autumn 2012
TMA4115 3 sp Autumn 2012
TMA4101 3.7 sp Autumn 2020
TMA4106 3.7 sp Autumn 2020
This course has academic overlap with the courses in the table above. If you take overlapping courses, you will receive a credit reduction in the course where you have the lowest grade. If the grades are the same, the reduction will be applied to the course completed most recently.

Subject areas

  • Mathematics

Contact information

Course coordinator

Lecturers

Department with academic responsibility

Department of Mathematical Sciences

Department with administrative responsibility

Pro-Rector for Education