# MA1201 - Linear Algebra and Geometry

### Examination arrangement

Examination arrangement: School exam

Evaluation Weighting Duration Grade deviation Examination aids
School exam 100/100 4 hours D

### Course content

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

Lectures and compulsory exercises.

• Exercises

### Further on evaluation

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

### Course materials

Will be announced at the start of the course.

### Credit reductions

Course code Reduction From To
MNFMA108 7.5
MA6201 7.5
TMA4110 3.0 AUTUMN 2009
TMA4115 3.0 AUTUMN 2009
MA0003 1.5 AUTUMN 2009
TMA4101 3.7 AUTUMN 2020
TMA4106 3.7 AUTUMN 2020
More on the course
Facts

Version: 1
Credits:  7.5 SP
Study level: Foundation courses, level I

Coursework

Term no.: 1
Teaching semester:  AUTUMN 2023

Language of instruction: -

Location: Trondheim

Subject area(s)
• Mathematics
Contact information
Course coordinator:

Department of Mathematical Sciences

# Examination

#### Examination arrangement: School exam

Term Status code Evaluation Weighting Examination aids Date Time Examination system
Autumn ORD School exam 100/100 2023-11-28 09:00
Summer UTS School exam 100/100
• * 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.
Examination

For more information regarding registration for examination and examination procedures, see "Innsida - Exams"

More on examinations at NTNU