## Example №2. Solving of a System of Linear Equations by the Gauss Elimination (Many Solutions)This solution has been made using the calculator presented on the site. Example №1. Solving of a system of linear equations by the Gauss elimination (one solution) Example №3. Solving of a system of linear equations by the Gauss elimination (no solution) 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 -4 is added to the equation 2. more info ( 8 x _{1} + 2 x_{1} * ( -4) ) + ( 12 x _{2} + 3 x_{2} * ( -4) ) + ( -9 x _{3} + ( - x_{3}) * ( -4) ) + ( 8 x _{4} + x_{4} * ( -4) ) = 3 + 1 * ( -4) The "red" coefficient is zero.
The equation 1 multiplied by -2 is added to the equation 3. more info ( 4 x _{1} + 2 x_{1} * ( -2) ) + ( 6 x _{2} + 3 x_{2} * ( -2) ) + ( 3 x _{3} + ( - x_{3}) * ( -2) ) + ( -2 x _{4} + x_{4} * ( -2) ) = 3 + 1 * ( -2) The "red" coefficient is zero.
The equation 1 multiplied by -1 is added to the equation 4. more info ( 2 x _{1} + 2 x_{1} * ( -1) ) + ( 3 x _{2} + 3 x_{2} * ( -1) ) + ( 9 x _{3} + ( - x_{3}) * ( -1) ) + ( -7 x _{4} + x_{4} * ( -1) ) = 3 + 1 * ( -1) The "red" coefficient is zero.
The equation 2 is added to the equation 3. more info ( 5 x _{3} + ( -5 x_{3}) ) + ( -4 x _{4} + 4 x_{4} ) = 1 + ( -1) The "red" coefficient is zero.
The equation 2 multiplied by 2 is added to the equation 4. more info ( 10 x _{3} + ( -5 x_{3}) * 2 ) + ( -8 x _{4} + 4 x_{4} * 2 ) = 2 + ( -1) * 2 The "red" coefficient is zero.
We will find the variable x _{3} from equation 2 of the system. - 5 x _{3} + 4 x_{4} = - 1 x _{3} = 1/5 + 4/5 x_{4} We will find the variable x _{1} from equation 1 of the system. 2 x _{1} + 3 x_{2} - x_{3} + x_{4} = 1 2 x _{1} = 1 - 3 x_{2} + x_{3} - x_{4}2 x _{1} = 1 - 3 x_{2} + ( 1/5 + 4/5 x_{4} ) - x_{4}x _{1} = 3/5 - 3/2 x_{2} - 1/10 x_{4}Result: x _{1} = 3/5 - 3/2 x_{2} - 1/10 x_{4}x
_{3} = 1/5 + 4/5 x_{4}© 2010-2021 If you have any comments, please write to siteReshmat@yandex.ru |