detailed information: The input equation set is: Question solving process:
Divide the two sides of equation (1) by 8, the equation can be obtained: | -1 | A | + | | | 1 2 | B | | - | 1 4 | C | + | | | 1 8 | D | = | | | 3 8 | (5) | , then add the two sides of equation (5) to both sides of equation (2), the equations are reduced to:
Multiply both sides of equation (1) by 3 Divide the two sides of equation (1) by 2, the equation can be obtained: | -12 | A | + | | 6 | B | | -3 | C | + | | | 3 2 | D | = | | | 9 2 | (6) | , then add the two sides of equation (6) to both sides of equation (3), the equations are reduced to:
Multiply both sides of equation (1) by 3 Divide the two sides of equation (1) by 8, the equation can be obtained: | -3 | A | + | | | 3 2 | B | | - | 3 4 | C | + | | | 3 8 | D | = | | | 9 8 | (7) | , then add the two sides of equation (7) to both sides of equation (4), the equations are reduced to:
Multiply both sides of equation (2) by 4 Divide the two sides of equation (2) by 3, the equation can be obtained: , then subtract both sides of equation (8) from both sides of equation (3), the equations are reduced to:
Multiply both sides of equation (2) by 7 Divide the two sides of equation (2) by 3, the equation can be obtained: | | | 7 2 | B | + | | | 7 4 | C | + | | | 21 8 | D | = | | | 7 8 | (9) | , then subtract both sides of equation (9) from both sides of equation (4), the equations are reduced to:
Divide the two sides of equation (3) by 2, the equation can be obtained: , then subtract both sides of equation (10) from both sides of equation (4), the equations are reduced to:
Divide both sides of equation (4) by 2, get the equation:, then add the two sides of equation (11) to both sides of equation (2), get the equation:
Multiply both sides of equation (4) by 4 Divide both sides of equation (4) by 9, get the equation:, then add the two sides of equation (12) to both sides of equation (1), get the equation:
Divide both sides of equation (3) by 4, get the equation:, then add the two sides of equation (13) to both sides of equation (2), get the equation:
Multiply both sides of equation (3) by 2 Divide both sides of equation (3) by 3, get the equation:, then subtract both sides of equation (14) from both sides of equation (1), get the equation:
Multiply both sides of equation (2) by 8 Divide both sides of equation (2) by 3, get the equation:, then subtract both sides of equation (15) from both sides of equation (1), get the equation:
The coefficient of the unknown number is reduced to 1, and the equations are reduced to:
Therefore, the solution of the equation set is:
Convert the solution of the equation set to decimals:
解方程组的详细方法请参阅:《多元一次方程组的解法》 |