Linear algebra is central to almost all areas of mathematics. For instance, linear algebra is fundamental in modem presentations of geometry. including for defining basic objects such as lines, planes, and rotations. Also, the functional analysis may be basically viewed as the application of linear algebra to spaces of functions. Linear algebra is also used in most sciences and engineering areas, because it allows modeling many natural phenomena, and efficiently computing with such models. For nonlinear systems, which cannot be modeled With linear algebra, linear algebra is often used for dealing with first-order approximations, using the fact that the differential of a multivariate function at a point is the linear map that best approximates the function near that point. The aim of the course is to arrange data in tabular forms. The course is designed for use of mathematical concepts in problem-solving through matrices. This course is designed to leam special techniques of matrices. This course will provide a foundation of important mathematical ideas in particular arrangements. This focuses on making connections among the various conceptual and numerical formations. To review the knowledge and practice the skills acquired in Business. To understand the concept of matrices and determinants with their applications.

**Contents**

1. Quadratic Functions and Complex Numbers

2. Linear Equations and Quadratic Equations: Formation of Linear equation

3. Solving a Linear equation involving one variable

4. Quadratic equation solved by factorization, square completion methods, quadratic formula

5. Matrices, Algebra of matrices, Inverses of matrices, Elementary row operations in matrices.

6. Ranks and transformation in matrices, System of linear equations, Gaussian elimination method

7.Gauss Gordan method, Determinants of squares matrices.

8. Determinants, Order of matrices, Decomposition of matrices: Transpose of a matrix.

9. Crammer rule, Eigenvalues and Eigenvectors, Bases, Dimension of a vector space, Linear Transformation, Orthogonal subspaces, Nullity of a linear transformation, Similar matrices.

10. Vector differential calculus, Gradient, Divergence, and curl, and concepts of vector integral calculus.

**Recommended Texts**

1. Anton, H. (2014). Elementary linear algebra, applications version. New York: John Wiley and Sons.

2. Schneider, H., & Barker, G. P. (1989). Matrices and linear algebra. North Chelmsford: Courier Corporation.