Linear Algebra and Differential Equations

Systems of linear equations, Elimination methods, matrices and matrix operations. Invertible matrices, determinants. Vector spaces, basis and dimension. Inner product spaces, orthogonality, orthogonal basis, rank and nullity. Eigenvalues and eigenvectors, systems of differential equations, matrix-valued functions. First and second order linear differential equations. n-th order linear differential equations, method of undetermined coefficient, variation of parameters.