Vector spaces: subspaces and linear independence, basis and dimension, row equivalence of matrices, general theorems about vector spaces, systems of linear equations, linear manifolds. Linear transformations: addition and multiplication, matrices of linear transformations. Inner products: angle and orthogonality, Gram-Schmidt orthogonalization, orthogonal transformations. Determinants: existence and uniqueness, multiplication theorem. 3 hours lecture. Prerequisite: 21-127.