Course topics

  1. Fields: the definition of a field, complex numbers.

  2. Linear equations: elementary operations, row reduction, homogeneous and non-homogeneous equations, parametrization of solutions.

  3. Vector spaces: examplex, subspaces, linear independence, bases, dimension.

  4. Matrix algebra: matrix addition and multiplication, elementary operations, the inverse matrix, the determinant and Cramer’s law. Linear transformations: examples, kernel and image, matrix representation.