At the end of this course, a student should acquire 

• the basic knowledge about vector spaces and subspaces,
• the basic knowledge about linear dependence/ independence  of sets of vectors and bases for vector spaces,
• the basic knowledge about matrix algebra and determinants,
• the knowledge and the basic skills about solving systems of linear equations systematically,
• basics of algebra of linear transformations and dual spaces,
• basics of representations of linear transformations by matrices.