Introduction to systems of linear equations.
Gaussian elimination.
Definition of matrices. Algebra of matrices.
Transpose of a matrix and inverse of matrix. Factorization.
Determinants. Quadratic forms.
Matrix polynomials. Euclidean n-space. Linear transformation from IRn to IRm .
Properties of linear transformation from IRn to IRm .
Real vector spaces and subspaces. Basis and dimension.
Rank and nullity. Inner product spaces. Gram-Schmidt process and QR-decomposition.
Eigenvalues and eigenvectors. Diagonalization.
Linear transformations. Kernel and Range.
Application of linear algebra to electric networks.