Vector spaces over the field and their subspaces. Intersections and linear, resp. direct sums. Linear combination of vectors, spanning sets, linear dependence and independence. Steinitz theorem, basis and dimension of a vector space.
Matrix over a field, type and rank of a matrix. Operations with matrices, transposed, inverse, regular and singular matrices.

Systems of linear equations over a field, homogeneous and nonhomogeneous, solvability.

Permutations. Determinant of a matrix. Cofactors and adjoints. Laplace expansion. Determinants and matrix inverses. Cramer rule.