Service for Solving Linear Programming Problems

and other interesting typical problems
Русский

Example №4. Solving of a System of Linear Equations by the Gauss Jordan Elimination (One Solution)

This solution was made using the calculator presented on the site.
Please note that the coefficients will disappear which located in the "red" positions.
Знак системы4x1+2x2- 3 x3 = - 3
5x1+3x2- 5 x3 = - 8
4x1+x2+5x3 = 22
The equation 1 multiplied by -1 is added to the equation 2.   more info
( 5 x1 + 4 x1 * ( -1) )
+ ( 3 x2 + 2 x2 * ( -1) )
+ ( -5 x3 + ( -3 x3) * ( -1) )
= -8 + ( -3) * ( -1)
This transformation will allow us to count without fractions for some time.
Знак системы4x1+2x2- 3 x3 = - 3
x1 +x2- 2 x3 = - 5
4x1+x2+5x3 = 22
The equation 2 and equation 1 are reversed.
Знак системыx1 +x2- 2 x3 = - 5
4x1+2x2- 3 x3 = - 3
4x1+x2+5x3 = 22
The equation 1 multiplied by -4 is added to the equation 2.   more info
( 4 x1 + x1 * ( -4) )
+ ( 2 x2 + x2 * ( -4) )
+ ( -3 x3 + ( -2 x3) * ( -4) )
= -3 + ( -5) * ( -4)
The "red" coefficient is zero.
Знак системыx1 +x2- 2 x3 = - 5
- 2 x2+5x3 = 17
4x1+x2+5x3 = 22
The equation 1 multiplied by -4 is added to the equation 3.   more info
( 4 x1 + x1 * ( -4) )
+ ( x2 + x2 * ( -4) )
+ ( 5 x3 + ( -2 x3) * ( -4) )
= 22 + ( -5) * ( -4)
The "red" coefficient is zero.
Знак системыx1 +x2- 2 x3 = - 5
- 2 x2+5x3 = 17
- 3 x2+13x3 = 42
The equation 3 multiplied by -1 is added to the equation 2.   more info
( -2 x2 + ( -3 x2) * ( -1) )
+ ( 5 x3 + 13 x3 * ( -1) )
= 17 + 42 * ( -1)
This transformation will allow us to count without fractions for some time.
Знак системыx1 +x2- 2 x3 = - 5
x2 - 8 x3 = - 25
- 3 x2+13x3 = 42
The equation 2 multiplied by 3 is added to the equation 3.   more info
( -3 x2 + x2 * 3 )
+ ( 13 x3 + ( -8 x3) * 3 )
= 42 + ( -25) * 3
The "red" coefficient is zero.
Знак системыx1 +x2- 2 x3 = - 5
x2 - 8 x3 = - 25
- 11 x3 = - 33
The equation 3 is divided by -11.
Знак системыx1 +x2- 2 x3 = - 5
x2 - 8 x3 = - 25
x3 = 3
The equation 3 multiplied by 8 is added to the equation 2.   more info
x2
+ ( -8 x3 + x3 * 8 )
= -25 + 3 * 8
The "red" coefficient is zero.
Знак системыx1 +x2- 2 x3 = - 5
x2 = - 1
x3 = 3
The equation 3 multiplied by 2 is added to the equation 1.   more info
x1
+ x2
+ ( -2 x3 + x3 * 2 )
= -5 + 3 * 2
The "red" coefficient is zero.
Знак системыx1 +x2 = 1
x2 = - 1
x3 = 3
The equation 2 multiplied by -1 is added to the equation 1.   more info
x1
+ ( x2 + x2 * ( -1) )
= 1 + ( -1) * ( -1)
The "red" coefficient is zero.
Знак системыx1 = 2
x2 = - 1
x3 = 3
Result:
x1 = 2
x2 = - 1
x3 = 3






© 2010-2024

If you have any comments, please write to matematika1974@yandex.ru