detailed information: The input equation set is:
| | | - | 162 125 | x | + | | | 7 25 | y | + | | | 7 25 | z | = | | 0 | | (1) |
| | | 7 25 | x | | - | 7 25 | y | + | | | 7 25 | z | = | | 0 | | (2) |
| | | 32 25 | x | + | | | 7 25 | y | | - | 7 25 | z | = | | 0 | | (3) |
| Question solving process:
Multiply both sides of equation (1) by 35 Divide the two sides of equation (1) by 162, the equation can be obtained: | - | 7 25 | x | + | | | 49 810 | y | + | | | 49 810 | z | = | | 0 | (4) | , then add the two sides of equation (4) to both sides of equation (2), the equations are reduced to:
| | | - | 162 125 | x | + | | | 7 25 | y | + | | | 7 25 | z | = | | 0 | | (1) |
| - | 889 4050 | y | + | | | 1379 4050 | z | = | | 0 | | (2) |
| | | 32 25 | x | + | | | 7 25 | y | | - | 7 25 | z | = | | 0 | | (3) |
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Multiply both sides of equation (1) by 80 Divide the two sides of equation (1) by 81, the equation can be obtained: | - | 32 25 | x | + | | | 112 405 | y | + | | | 112 405 | z | = | | 0 | (5) | , then add the two sides of equation (5) to both sides of equation (3), the equations are reduced to:
| | | - | 162 125 | x | + | | | 7 25 | y | + | | | 7 25 | z | = | | 0 | | (1) |
| - | 889 4050 | y | + | | | 1379 4050 | z | = | | 0 | | (2) |
| | | 1127 2025 | y | | - | 7 2025 | z | = | | 0 | | (3) |
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Multiply both sides of equation (2) by 322 Divide the two sides of equation (2) by 127, the equation can be obtained: | - | 1127 2025 | y | + | | | 222019 257175 | z | = | | 0 | (6) | , then add the two sides of equation (6) to both sides of equation (3), the equations are reduced to:
| | | - | 162 125 | x | + | | | 7 25 | y | + | | | 7 25 | z | = | | 0 | | (1) |
| - | 889 4050 | y | + | | | 1379 4050 | z | = | | 0 | | (2) |
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Multiply both sides of equation (3) by 25019 Divide both sides of equation (3) by 63180, get the equation:, then subtract both sides of equation (7) from both sides of equation (2), get the equation:
| | | - | 162 125 | x | + | | | 7 25 | y | + | | | 7 25 | z | = | | 0 | | (1) |
| | |
Multiply both sides of equation (3) by 127 Divide both sides of equation (3) by 390, get the equation:, then subtract both sides of equation (8) from both sides of equation (1), get the equation:
Multiply both sides of equation (2) by 162 Divide both sides of equation (2) by 127, get the equation:, then add the two sides of equation (9) to 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:
解方程组的详细方法请参阅:《多元一次方程组的解法》 |