Service for Solving Linear Programming Problems

and other interesting typical problems
Русский

Example №5. Solving of a System of Linear Equations by the Gauss Jordan Elimination (Many Solutions)

This solution has been made using the calculator presented on the site.
Please note that the coefficients will disappear which located in the "red" positions.
 2 x1 + 3 x2 - x3 + x4 = 1 8 x1 + 12 x2 - 9 x3 + 8 x4 = 3 4 x1 + 6 x2 + 3 x3 - 2 x4 = 3 2 x1 + 3 x2 + 9 x3 - 7 x4 = 3
The equation 1 multiplied by -4 is added to the equation 2.   more info
( 8 x1 + 2 x1 * ( -4) )
+ ( 12 x2 + 3 x2 * ( -4) )
+ ( -9 x3 + ( - x3) * ( -4) )
+ ( 8 x4 + x4 * ( -4) )
= 3 + 1 * ( -4)
The "red" coefficient is zero.
 2 x1 + 3 x2 - x3 + x4 = 1 - 5 x3 + 4 x4 = - 1 4 x1 + 6 x2 + 3 x3 - 2 x4 = 3 2 x1 + 3 x2 + 9 x3 - 7 x4 = 3
The equation 1 multiplied by -2 is added to the equation 3.   more info
( 4 x1 + 2 x1 * ( -2) )
+ ( 6 x2 + 3 x2 * ( -2) )
+ ( 3 x3 + ( - x3) * ( -2) )
+ ( -2 x4 + x4 * ( -2) )
= 3 + 1 * ( -2)
The "red" coefficient is zero.
 2 x1 + 3 x2 - x3 + x4 = 1 - 5 x3 + 4 x4 = - 1 5 x3 - 4 x4 = 1 2 x1 + 3 x2 + 9 x3 - 7 x4 = 3
The equation 1 multiplied by -1 is added to the equation 4.   more info
( 2 x1 + 2 x1 * ( -1) )
+ ( 3 x2 + 3 x2 * ( -1) )
+ ( 9 x3 + ( - x3) * ( -1) )
+ ( -7 x4 + x4 * ( -1) )
= 3 + 1 * ( -1)
The "red" coefficient is zero.
 2 x1 + 3 x2 - x3 + x4 = 1 - 5 x3 + 4 x4 = - 1 5 x3 - 4 x4 = 1 10 x3 - 8 x4 = 2
The equation 2 is added to the equation 3.   more info
( 5 x3 + ( -5 x3) )
+ ( -4 x4 + 4 x4 )
= 1 + ( -1)
The "red" coefficient is zero.
 2 x1 + 3 x2 - x3 + x4 = 1 - 5 x3 + 4 x4 = - 1 0 = 0 10 x3 - 8 x4 = 2
The equation 2 multiplied by 2 is added to the equation 4.   more info
( 10 x3 + ( -5 x3) * 2 )
+ ( -8 x4 + 4 x4 * 2 )
= 2 + ( -1) * 2
The "red" coefficient is zero.
 2 x1 + 3 x2 - x3 + x4 = 1 - 5 x3 + 4 x4 = - 1 0 = 0 0 = 0
 2 x1 + 3 x2 - x3 + x4 = 1 - 5 x3 + 4 x4 = - 1
The equation 2 is divided by -5.
 2 x1 + 3 x2 - x3 + x4 = 1 x3 - 4/5 x4 = 1/5
The equation 2 is added to the equation 1.   more info
2 x1
+ 3 x2
+ ( - x3 + x3 )
+ ( x4 + ( -4/5 x4) )
= 1 + 1/5
The "red" coefficient is zero.
 2 x1 + 3 x2 + 1/5 x4 = 6/5 x3 - 4/5 x4 = 1/5
The equation 1 is divided by 2.
 x1 + 3/2 x2 + 1/10 x4 = 3/5 x3 - 4/5 x4 = 1/5
Result:
x1 = 3/5 - 3/2 x2 - 1/10 x4
x3 = 1/5 + 4/5 x4

© 2010-2021

If you have any comments, please write to siteReshmat@yandex.ru