# Unit IV: Solution of Linear Algebraic Equations | BCA 4th Semester Numerical Methods BCA Notes Pdf

The term "algebraic equation" refers to a formulation of the equality of two expressions using the algebraic operations of addition, subtraction, multiplication, division, raising to a power, and extraction of a root on a set of variables. The process of locating a number or group of numbers that, when substituted for the variables in the equation, reduce it to an identity is known as the solution of an algebraic equation. A root of the equation is an integer like this.

According to the number of solutions, systems of linear algebraic equations are split into the following types:

1. a compatible system is a system of linear equations having at least one solution;
2. an incompatible (or contradictory) system is a system having no solution;
3. a determinate system is a system having a unique solution;
4. an indeterminate system is a system having more than one solution.

Every indeterminate system of linear equations has an unlimited number of solutions if one takes into account solutions of a system with values of the unknowns in a specified number field (or in any arbitrary infinite field). The type of a system of linear algebraic equations does not change when the provided field P is expanded, in contrast to equations of degree greater than one. Therefore, a system that is incompatible with another system cannot become compatible with it, and a system that is determined cannot become uncertain. However, this expands the possible solutions for an indeterminate system.

In this “Solution of Linear Algebraic Equations - Numerical Methods” you will learn about the following topics:

1. Matrices and their properties
2. Elimination methods, Gauss Jordan method, pivoting
3. Method of factorization: Dolittle, Crout’s and Cholesky’s methods
4. The inverse of a matrix
5. Ill-Conditioned Systems
6. Iterative methods: Gauss Jacobi, Gauss seidel, Relaxation methods
7. Power method

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The article Solution of Linear Algebraic Equations - Numerical Methods is contributed by Namrata Chaudhary, a student of Lumbini Engineering College (LEC).

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