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Solving Linear Equations: Gaussian Elimination Method Example

Learn how to solve systems of linear equations using Gaussian elimination method in linear algebra with a step-by-step example. See how the method is applied to matrices of coefficients and find solutions efficiently.

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Solving Linear Equations: Gaussian Elimination Method Example

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  1. SYSTEM OF LINEAR EQUATIONS: Example: System of linear equations is frequently encountered in the solution of various engineering problems containing more than one unknown variables. In linear algebra, the Gaussian elimination method (also known as row reduction) is used to solve the system of linear equations. The method is a sequence of operations performed on the associated matrix of coefficients. Gaussian Elimination Method x1 x2 x3 3 2 0 14 12 13 6 40 Multiply by -1/4 and sum with 1st row -3 8 9 -28 Sum with 1st row 3 2 0 14 0 -5/4 -3/2 4 Multiply by 5/40 and sum with 2nd row 0 10 9 -14 3 2 0 14 0 -5/4 -3/2 4 0 0 -3/8 9/4

  2. System of Linear Equations: System of linear equations can be written in matrix form as x b A Solution with Matlab: x = 2.0000 4.0000 -6.0000 clc;clear; a=[3,2,0;12,13,6;-3,8,9]; b=[14;40;-28]; x=inv(a)*b

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