Solving Systems of Linear Equations

In Mathematics, simultaneous equations are a set of equations containing multiple variables. This set of equations is often referred to as a system of equations. A linear system is a set of linear equations and a homogeneous linear system is a set of homogeneous linear equations. Matrices are helpful in rewriting a linear system in a very simple form. The algebraic properties of matrices may then be used to solve systems. A very well-known technique used to solve simultaneous equations is the Gaussian Elimination Method. The Gauss Elimination method eliminates the variables and finally the set of equations is reduced into a lower triangular form. Linear equations are functions that have two variables. For solving simultaneous equations using the ‘elimination’ method, two equations are simplified by adding them or subtracting them. This eliminates one of the variables, so that the other variable can be found. Gauss elimination methods provides an algorithm for solving systems of linear equations. It can also be used to find the rank of a matrix. Elementary row operations are used to reduce a matrix to what is called a triangular form. The Gauss elimination method consists of Forward Elimination of Unknowns method and Back Substitution method to solve the equation. The goal of Forward Elimination is to transform the coefficient matrix into an upper triangular matrix.

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