Row Operations: a system of linear equations, row reduction, Gaussian elimination; Matrix: definition, matrix algebra, inverse matrix; Determinant: definition, cofactor expansion, Cramer’s rule; System of Linear Equations: matrix and determinant methods for finding the solution, overdetermined and underdetermined solutions; Vectors in Rn and Cn: a review of geometric vectors in R2 and R3 space, vectors in Rn and Cn, inner product, norm and distance in Rn and Cn; Vector Space: linear vector space, subspace; Linear Dependence and Independence: basis and dimension of vector spaces, row and column space of a matrix, the rank of matrices, solution spaces of systems of linear equations; Eigenvalues and Eigenvectors: characteristic equation, diagonalization, Cayley-Hamilton theorem, applications; General Linear Transformation: kernel and image of a linear transformation and their properties, matrix representation of linear transformations, change of bases, isomorphism, similarity; Inner Product Space: inner product, angle, and orthogonality, Gram-Schmidt procedure