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Example №3. Solving of a System of Linear Equations by the Gauss elimination (No Solution)

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.
Знак системыx1 - 2 x2+3x3- 4 x4 = 2
3x1+3x2- 5 x3+x4 = - 3
- 2 x1+x2+2x3- 3 x4 = 5
3x1+3x3- 10 x4 = 8
The equation 1 multiplied by -3 is added to the equation 2.   more info
( 3 x1 + x1 * ( -3) )
+ ( 3 x2 + ( -2 x2) * ( -3) )
+ ( -5 x3 + 3 x3 * ( -3) )
+ ( x4 + ( -4 x4) * ( -3) )
= -3 + 2 * ( -3)
The "red" coefficient is zero.
Знак системыx1 - 2 x2+3x3- 4 x4 = 2
9x2- 14 x3+13x4 = - 9
- 2 x1+x2+2x3- 3 x4 = 5
3x1+3x3- 10 x4 = 8
The equation 1 multiplied by 2 is added to the equation 3.   more info
( -2 x1 + x1 * 2 )
+ ( x2 + ( -2 x2) * 2 )
+ ( 2 x3 + 3 x3 * 2 )
+ ( -3 x4 + ( -4 x4) * 2 )
= 5 + 2 * 2
The "red" coefficient is zero.
Знак системыx1 - 2 x2+3x3- 4 x4 = 2
9x2- 14 x3+13x4 = - 9
- 3 x2+8x3- 11 x4 = 9
3x1+3x3- 10 x4 = 8
The equation 1 multiplied by -3 is added to the equation 4.   more info
( 3 x1 + x1 * ( -3) )
- 2 x2 * ( -3)
+ ( 3 x3 + 3 x3 * ( -3) )
+ ( -10 x4 + ( -4 x4) * ( -3) )
= 8 + 2 * ( -3)
The "red" coefficient is zero.
Знак системыx1 - 2 x2+3x3- 4 x4 = 2
9x2- 14 x3+13x4 = - 9
- 3 x2+8x3- 11 x4 = 9
6x2- 6 x3+2x4 = 2
The equation 3 and equation 2 are reversed.
Знак системыx1 - 2 x2+3x3- 4 x4 = 2
- 3 x2+8x3- 11 x4 = 9
9x2- 14 x3+13x4 = - 9
6x2- 6 x3+2x4 = 2
The equation 2 multiplied by 3 is added to the equation 3.   more info
( 9 x2 + ( -3 x2) * 3 )
+ ( -14 x3 + 8 x3 * 3 )
+ ( 13 x4 + ( -11 x4) * 3 )
= -9 + 9 * 3
The "red" coefficient is zero.
Знак системыx1 - 2 x2+3x3- 4 x4 = 2
- 3 x2+8x3- 11 x4 = 9
10x3- 20 x4 = 18
6x2- 6 x3+2x4 = 2
The equation 2 multiplied by 2 is added to the equation 4.   more info
( 6 x2 + ( -3 x2) * 2 )
+ ( -6 x3 + 8 x3 * 2 )
+ ( 2 x4 + ( -11 x4) * 2 )
= 2 + 9 * 2
The "red" coefficient is zero.
Знак системыx1 - 2 x2+3x3- 4 x4 = 2
- 3 x2+8x3- 11 x4 = 9
10x3- 20 x4 = 18
10x3- 20 x4 = 20
The equation 3 multiplied by -1 is added to the equation 4.   more info
( 10 x3 + 10 x3 * ( -1) )
+ ( -20 x4 + ( -20 x4) * ( -1) )
= 20 + 18 * ( -1)
The "red" coefficient is zero.
Знак системыx1 - 2 x2+3x3- 4 x4 = 2
- 3 x2+8x3- 11 x4 = 9
10x3- 20 x4 = 18
0 = 2
Equation 4 is false. The system has no solution.








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