|Owning Department/School:||Department of Mathematical Sciences|
|Level:||Certificate (FHEQ level 4)|
|Supplementary Assessment:||MA10210 Mandatory extra work (where allowed by programme regulations)|
|Requisites:||Before taking this unit you must take MA10209 and while taking this unit you must take MA10207|
To provide a firm grounding in linear algebra, both practically via matrices and abstractly via vector spaces and linear maps.
After taking this unit the students should be able to:
* Demonstrate understanding of abstract concepts of elementary linear algebra, (e.g. linear independence, dimension) and apply abstract ideas in specific examples.
* Solve systems of linear equations.
* Compute determinants, matrix inverses, eigenvalues and eigenvectors.
Numeracy T/F A
Problem Solving T/F A
Written and Spoken Communication F (in tutorials).
Systems of linear equations: matrix representation, row echelon form. Linear algebra and geometry in R2 and R3. Matrices as linear maps. Axiomatic development of vector spaces. Linear maps and subspaces, kernel and image. Linear independence and bases.
Linear maps as matrices, change of basis, similar matrices.
Dimension, rank, nullity. Rank-Nullity theorem.
Determinants: definition, properties and computation. Adjugate and inverse formula. Invertibility of matrices. Cramer's rule.
Eigenvalues, eigenvectors and eigenspaces. Characteristic polynomial.
Algebraic and geometric multiplicities. Diagonalisation.
MA10210 is Compulsory on the following programmes:Department of Computer Science