244 ريض - الجبر الخطي - Linear Algebra

Course Outline:

1. Matrices and Determinants:

1. Matrices and matrix operations; elementary row and column operations; inverse of a matrix; special matrices.
2. Definition of determinant of a matrix; evaluation of a determinant; properties of determinants; adjoint of a matrix and its properties.
3. Systems of linear equations: Gauss and Gauss – Jordan elimination methods; homogeneous systems of linear equations; Cramer’s Rule.

2. Vector Spaces and Inner Product Spaces:

1. Definition of a vector space and examples; subspaces; linear combinations and linear span of a sets of vectors; linear dependence and linear independence of a set of vectors; basis and dimension of a vector space; coordinates of a vector with respect to a basis; change of basis; rank and nullity of a matrix.
2. Definition of inner product and inner product space with examples; orthogonal and orthonormal sets of vectors; orthonormal basis; Gram-Schmidt orthonormalization process.

3. Linear Transformations and Diagonalizable Matrices:

1. Definition of a linear transformation and examples; basic properties of linear transformations; kernel and image spaces of a linear transformation; matrix of linear transformation.
2. Eigenvalues and eigenvectors of a matrix; diagonalization of a matrix.

 

Recommended Book: “Elementary Linear Algebra (Applications Version)” by Howard Anton and Chris Rorres, 11th Edition, Wiley, USA, 2014 (To download the book).