MATH-244: Linear Algebra

King Saud University / Department of Mathematics
Math-244 (Linear Algebra) / Semester 2 of Academic Year 1444H

Course Outline:

Weeks 1-4: Matrices and Determinants: Matrices and matrix operations; elementary row and column operations; inverse of a matrix; special matrices. Definition of determinant of a matrix; evaluation of a determinant; properties of determinants; adjoint of a matrix and its properties. Systems of linear equations: Gauss and Gauss – Jordan elimination methods; homogeneous systems of linear equations; Cramer’s Rule.

Weeks 5-7: Vector Spaces and Inner Product Spaces: 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. Definition of inner product and inner product space with examples; orthogonal and orthonormal sets of vectors; orthonormal basis; Gram-Schmidt orthonormalization process.

Weeks 8-10: Linear Transformations and Diagonalizable Matrices: Definition of a linear transformation and examples; basic properties of linear transformations; kernel and image spaces of a linear transformation; matrix of linear transformation. 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.

Exercises (from the recommended book): Exercise Set 1.1: 1-23 (odd); Exercise Set 1.2: 1-32 (odd); Exercise Set 1.3: 1-6 (all) and 9-27 (odd); Exercise Set 1.4: 1-33 (odd); Exercise Set 1.5: 2-20 (even); Exercise Set 1.6: 9-20 (all); Exercise Set 1.7: 1-25 (odd); Exercise Set 2.1: 1-31 (odd); Exercise Set 2.2: 2-30 (even); Exercise Set 2.3: 2-32 (even); Exercise Set 4.1: 1-15 (odd); Exercise Set 4.2: 1-9(all) and 10-22 (even); Exercise Set 4.3:112(all); Exercise Set 4.4: 1-22 (all); Exercise Set 4.5: 1-20 (all); Exercise Set 4.6: 1-10 (all); Exercise Set 4.7: 1-21 (odd); Exercise Set 4.8: 1-21 (odd); Exercise Set 4.10: 5-10 (all) and 11-19(odd); Exercise Set 5.1: 1-14 (all); Exercise Set 5.2: 2-20 (all).

Quiz 1: Date: Sunday 01/6/1444H (25/12/2022G) at the scheduled class time. Contents: Matrices, Determinants and Linear Systems.

Mid-term Exam: Date: Monday 01/7/1444H (23/01/2023G) at 7:00PM. Contents: Matrices, Determinants, linear systems and Vector Spaces.

Quiz 2: Thursday 11/7/1444H (02/02/2023G) at the scheduled class time. Contents: Vector Spaces and inner Product Spaces.

Final Exam: Date: Sunday 28/7/1444H (19/02/2023G) at 1:00PM. Contents: Complete course contents.