Vectors and operations in R and R. Matrices and operations, systems of linear equations, Gaussian elimination, Gauss-Jordan method for matrix inversion. Determinants, cofactors, applications to inverting a matrix. Euclidean n-space, linear combinations, dependence and independence, basis, dimension, row and column spaces of a matrix, rank, orthonormal bases, Gram-Schmidt orthonormalisation, change of basis. Linear transformations, matrix format, kernel and image, detailed study of operators on R, eigenvectors and eigenvalues of linear operators on R, similar matrices, diagonalisation.
Contact hours:
5 lectures/tutorials per week.Assessment:
2 tests (25%), 3 assignments (15%) and final exam (60%).