Systems of linear equations. Matrices. Algebraic properties of matrix operations. Special types of matrices. Solving systems of linear equations. Finding the inverse of a matrix. Equivalent matrices. Determinants. Properties of determinants. Vectors in the plane and in 3-space. Vector spaces. Subspaces. Span and linear independence. Basis and dimension. Row space. Null space. Nullity and rank of a matrix. Linear transformations. Kernel and range of a linear transformation. Eigenvalues and eigenvectors.