Vektorit ja matriisit, Lectures in English
Final exam is worth 75% of the course grade. The exam will be an electronic EXAM, closed-book, with no calculator allowed. Weekly homework assignments are worth 15% of the course grade. Active participation in exercise sessions is worth 10% of the course grade.
Alternatively, electronic EXAM can be taken to pass the course. This option is primarily meant for students that want to self-study the course (e.g. in spring semester).
Osallistuminen opetukseen (englanti)
Vectors: geometry and algebra of vectors; length, angle, dot product, projections; lines and planes.
Linear equations: augmented matrix, Gaussian and Gauss-Jordan elimination, spanning sets and linear independence, applications.
Matrix addition, scalar multiplication, multiplication, block multiplication, power, transpose.
Inverse and rank of matrices: inverse properties, elementary matrices, Gauss-Jordan method for inverse; subspace, column space, row space, null space, basis, dimension, rank, nullity, conditions for invertibility, coordinates with respect to a basis.
Determinant of a matrix: cofactor expansion formula, determinant properties, matrix invertibility; Leslie population model; cross product and scalar triple product.
Eigenvalues and eigenvectors, algebraic multiplicity, geometric multiplicity; similar matrices, diagonalisation, powers of a diagonalisable matrix.