SYSTEM OF LINEAR EQUATIONS:

Gaussian Elimination Method

Example:

21 x214x3

040x6x13x12 321

312 x9x328x8

x1 x2 x3

3 2 0 14

12 13 6 40

-3 8 9 -28

3 2 0 14

0 -5/4 -3/2 4

0 10 9 -14

Multiply by -1/4 and sum with 1st row

Sum with 1st row

Multiply by 5/40 and sum with 2nd row

3 2 0 14

0 -5/4 -3/2 4

0 0 -3/8 9/4 4

9x8

33 6x3

4)6(2

3x4

52 4x2

14042x3 1 2x1

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.

21 x214x3

040x6x13x12 321

312 x9x328x8

28

40

14

x

x

x

983

61312

023

3

2

1

System of Linear Equations:

System of linear equations can be written in matrix form as

bxA A x b

bAx 1

clc;clear;a=[3,2,0;12,13,6;-3,8,9];b=[14;40;-28];x=inv(a)*b

Solution with Matlab:

x =

2.0000 4.0000 -6.0000