Example №3. Solving of a System of Linear Equations by the Gauss elimination (No Solution)This solution was made using the calculator presented on the site. Example №1. Solving of a system of linear equations by the Gauss elimination (one solution) Example №2. Solving of a system of linear equations by the Gauss elimination (many solutions) Example №4. Solving of a system of linear equations by the Gauss Jordan elimination (one solution) Example №5. Solving of a system of linear equations by the Gauss Jordan elimination (many solutions) Please note that the coefficients will disappear which located in the "red" positions.
The equation 1 multiplied by 3 is added to the equation 2. more info ( 3 x_{1} + x_{1} * ( 3) ) + ( 3 x_{2} + ( 2 x_{2}) * ( 3) ) + ( 5 x_{3} + 3 x_{3} * ( 3) ) + ( x_{4} + ( 4 x_{4}) * ( 3) ) = 3 + 2 * ( 3) The "red" coefficient is zero.
The equation 1 multiplied by 2 is added to the equation 3. more info ( 2 x_{1} + x_{1} * 2 ) + ( x_{2} + ( 2 x_{2}) * 2 ) + ( 2 x_{3} + 3 x_{3} * 2 ) + ( 3 x_{4} + ( 4 x_{4}) * 2 ) = 5 + 2 * 2 The "red" coefficient is zero.
The equation 1 multiplied by 3 is added to the equation 4. more info ( 3 x_{1} + x_{1} * ( 3) )  2 x_{2} * ( 3) + ( 3 x_{3} + 3 x_{3} * ( 3) ) + ( 10 x_{4} + ( 4 x_{4}) * ( 3) ) = 8 + 2 * ( 3) The "red" coefficient is zero.
The equation 3 and equation 2 are reversed.
The equation 2 multiplied by 3 is added to the equation 3. more info ( 9 x_{2} + ( 3 x_{2}) * 3 ) + ( 14 x_{3} + 8 x_{3} * 3 ) + ( 13 x_{4} + ( 11 x_{4}) * 3 ) = 9 + 9 * 3 The "red" coefficient is zero.
The equation 2 multiplied by 2 is added to the equation 4. more info ( 6 x_{2} + ( 3 x_{2}) * 2 ) + ( 6 x_{3} + 8 x_{3} * 2 ) + ( 2 x_{4} + ( 11 x_{4}) * 2 ) = 2 + 9 * 2 The "red" coefficient is zero.
The equation 3 multiplied by 1 is added to the equation 4. more info ( 10 x_{3} + 10 x_{3} * ( 1) ) + ( 20 x_{4} + ( 20 x_{4}) * ( 1) ) = 20 + 18 * ( 1) The "red" coefficient is zero.
Equation 4 is false. The system has no solution.
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