detailed information: The input equation set is:
| | | - | 162 125 | A | + | | | 7 25 | B | + | | | 7 25 | C | = | | 0 | | (1) |
| | | 7 25 | A | | - | 7 25 | B | + | | | 7 25 | C | = | | 0 | | (2) |
| | | 32 25 | A | + | | | 7 25 | B | | - | 7 25 | C | = | | 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 | A | + | | | 49 810 | B | + | | | 49 810 | C | = | | 0 | (5) | , then add the two sides of equation (5) to both sides of equation (2), the equations are reduced to:
| | | - | 162 125 | A | + | | | 7 25 | B | + | | | 7 25 | C | = | | 0 | | (1) |
| - | 889 4050 | B | + | | | 1379 4050 | C | = | | 0 | | (2) |
| | | 32 25 | A | + | | | 7 25 | B | | - | 7 25 | C | = | | 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 | A | + | | | 112 405 | B | + | | | 112 405 | C | = | | 0 | (6) | , then add the two sides of equation (6) to both sides of equation (3), the equations are reduced to:
| | | - | 162 125 | A | + | | | 7 25 | B | + | | | 7 25 | C | = | | 0 | | (1) |
| - | 889 4050 | B | + | | | 1379 4050 | C | = | | 0 | | (2) |
| | | 1127 2025 | B | | - | 7 2025 | C | = | | 0 | | (3) |
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Multiply both sides of equation (1) by 125 Divide the two sides of equation (1) by 162, the equation can be obtained: | -1 | A | + | | | 35 162 | B | + | | | 35 162 | C | = | | 0 | (7) | , then add the two sides of equation (7) to both sides of equation (4), the equations are reduced to:
| | | - | 162 125 | A | + | | | 7 25 | B | + | | | 7 25 | C | = | | 0 | | (1) |
| - | 889 4050 | B | + | | | 1379 4050 | C | = | | 0 | | (2) |
| | | 1127 2025 | B | | - | 7 2025 | C | = | | 0 | | (3) |
| | | 197 162 | B | + | | | 197 162 | C | = | | 1 | | (4) |
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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 | B | + | | | 222019 257175 | C | = | | 0 | (8) | , then add the two sides of equation (8) to both sides of equation (3), the equations are reduced to:
| | | - | 162 125 | A | + | | | 7 25 | B | + | | | 7 25 | C | = | | 0 | | (1) |
| - | 889 4050 | B | + | | | 1379 4050 | C | = | | 0 | | (2) |
| | | | 197 162 | B | + | | | 197 162 | C | = | | 1 | | (4) |
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Multiply both sides of equation (2) by 4925 Divide the two sides of equation (2) by 889, the equation can be obtained: | - | 197 162 | B | + | | | 38809 20574 | C | = | | 0 | (9) | , then add the two sides of equation (9) to both sides of equation (4), the equations are reduced to:
| | | - | 162 125 | A | + | | | 7 25 | B | + | | | 7 25 | C | = | | 0 | | (1) |
| - | 889 4050 | B | + | | | 1379 4050 | C | = | | 0 | | (2) |
| | |
Multiply both sides of equation (3) by 125095 Divide the two sides of equation (3) by 34671, the equation can be obtained: , then subtract both sides of equation (10) from both sides of equation (4), the equations are reduced to:
| | | - | 162 125 | A | + | | | 7 25 | B | + | | | 7 25 | C | = | | 0 | | (1) |
| - | 889 4050 | B | + | | | 1379 4050 | C | = | | 0 | | (2) |
| | 0 = | | | 1948746977 1948746977 | | (4) |
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由第(4)方程式可以看出,该方程组无解。
解方程组的详细方法请参阅:《多元一次方程组的解法》 |