الجبر الخطي 1- UQU

1 Linear Equations and Systems: / System of linear equations / Solutions: consistent, inconsistent, unique, infinite solutions / Row eeduction and echelon forms / Gaussian and Gauss-Jordan elimination 2 Matrices and Determinants: / Definintion and types of matrices (square, diagonal, identity, elementary, etc.) / Matrix operation: addition, multiplication, scalar multiplication / Transpose of of a matrix / Determinants: properties, computation, and applications / Minors and Cofactors / Inverse of a matrix (via adjoint or row reduction) 3 Vecors and Vector Spaces: / Definition of vectors / Operations: addition, scalar multiplication / Vector spaces and subspaces / Linear cominations and spans / Basis and dimension 4 Linear Independence / Definition of linear idependence and dependence / Relation to basis and spans 5 Linear Transformations / Definitions and examples / Kernal and range 6 Eigenvalues and eigenvectors: / Definition and properties / Characteristic polynomial