The aim of this module is to introduce students to the main ideas of Linear Algebra and its many applications. The emphasis is on developing the student's ability to perform calculations on and with matrices, particularly 2x2 and 3x3 matrices, and on and with vectors in 2 and 3 dimensions. These ideas are then extended to higher dimensions.

Matrices: introduction to matrices, matrix algebra, transpose of a matrix, symmetric matrices, invertible matrices and their inverses, determinants. Vectors in 2 and 3 dimensions: geometric interpretation of vectors, vector arithmetic, Euclidean norm, Euclidean scalar product, angle, orthogonality, projections, cross product and its uses in the study of lines and planes in 3 dimensions. Lines and planes in 3-dimensional space: parametric equation of a line, distance between a point and a line, point-normal form and general form of the equation of a plane, distance between a point and a plane. Extension to vectors in n dimensions; Systems of linear equations and their solution: Gaussian elimination methods (Gauss, Gauss-Jordan) and inverse matrix method; Matrices acting on vectors: eigenvalues and eigenvectors particularly in 2 and 3 dimensions. Applications: least squares fit, rotation matrices.