detailed information: The input equation set is:
 | | | -3 | A | + | | B | + | | 5 | C | + | | | 7 50 | D | = | | 0 | | (1) |
| | A | | -3 | B | + | | 5 | C | + | | | 7 50 | D | = | | 0 | | (2) |
| | | 1 5 | A | + | | | 1 5 | B | | -3 | C | + | | | 1 5 | D | = | | 0 | | (3) |
| | Question solving process:
Divide the two sides of equation (1) by 3, the equation can be obtained: | -1 | A | + | | | 1 3 | B | + | | | 5 3 | C | + | | | 7 150 | D | = | | 0 | (5) | , then add the two sides of equation (5) to both sides of equation (2), the equations are reduced to:
 | | | -3 | A | + | | B | + | | 5 | C | + | | | 7 50 | D | = | | 0 | | (1) |
| - | 8 3 | B | + | | | 20 3 | C | + | | | 14 75 | D | = | | 0 | | (2) |
| | | 1 5 | A | + | | | 1 5 | B | | -3 | C | + | | | 1 5 | D | = | | 0 | | (3) |
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Divide the two sides of equation (1) by 15, the equation can be obtained: | - | 1 5 | A | + | | | 1 15 | B | + | | | 1 3 | C | + | | | 7 750 | D | = | | 0 | (6) | , then add the two sides of equation (6) to both sides of equation (3), the equations are reduced to:
 | | | -3 | A | + | | B | + | | 5 | C | + | | | 7 50 | D | = | | 0 | | (1) |
| - | 8 3 | B | + | | | 20 3 | C | + | | | 14 75 | D | = | | 0 | | (2) |
| | | 4 15 | B | | - | 8 3 | C | + | | | 157 750 | D | = | | 0 | | (3) |
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Multiply both sides of equation (1) by 7 Divide the two sides of equation (1) by 3, the equation can be obtained: | -7 | A | + | | | 7 3 | B | + | | | 35 3 | C | + | | | 49 150 | D | = | | 0 | (7) | , then add the two sides of equation (7) to both sides of equation (4), the equations are reduced to:
 | | | -3 | A | + | | B | + | | 5 | C | + | | | 7 50 | D | = | | 0 | | (1) |
| - | 8 3 | B | + | | | 20 3 | C | + | | | 14 75 | D | = | | 0 | | (2) |
| | | 4 15 | B | | - | 8 3 | C | + | | | 157 750 | D | = | | 0 | | (3) |
| | | 28 3 | B | + | | | 62 3 | C | | - | 401 150 | D | = | | 0 | | (4) |
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Divide the two sides of equation (2) by 10, the equation can be obtained: | - | 4 15 | B | + | | | 2 3 | C | + | | | 7 375 | D | = | | 0 | (8) | , then add the two sides of equation (8) to both sides of equation (3), the equations are reduced to:
 | | | -3 | A | + | | B | + | | 5 | C | + | | | 7 50 | D | = | | 0 | | (1) |
| - | 8 3 | B | + | | | 20 3 | C | + | | | 14 75 | D | = | | 0 | | (2) |
| | | | 28 3 | B | + | | | 62 3 | C | | - | 401 150 | D | = | | 0 | | (4) |
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Multiply both sides of equation (2) by 7 Divide the two sides of equation (2) by 2, the equation can be obtained: | - | 28 3 | B | + | | | 70 3 | C | + | | | 49 75 | D | = | | 0 | (9) | , then add the two sides of equation (9) to both sides of equation (4), the equations are reduced to:
 | | | -3 | A | + | | B | + | | 5 | C | + | | | 7 50 | D | = | | 0 | | (1) |
| - | 8 3 | B | + | | | 20 3 | C | + | | | 14 75 | D | = | | 0 | | (2) |
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Multiply both sides of equation (3) by 22, the equation can be obtained: , then add the two sides of equation (10) to both sides of equation (4), the equations are reduced to:
 | | | -3 | A | + | | B | + | | 5 | C | + | | | 7 50 | D | = | | 0 | | (1) |
| - | 8 3 | B | + | | | 20 3 | C | + | | | 14 75 | D | = | | 0 | | (2) |
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Multiply both sides of equation (4) by 57 Divide both sides of equation (4) by 749, get the equation:, then subtract both sides of equation (11) from both sides of equation (3), get the equation:
 | | | -3 | A | + | | B | + | | 5 | C | + | | | 7 50 | D | = | | 0 | | (1) |
| - | 8 3 | B | + | | | 20 3 | C | + | | | 14 75 | D | = | | 0 | | (2) |
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Multiply both sides of equation (4) by 20 Divide both sides of equation (4) by 321, get the equation:, then subtract both sides of equation (12) from both sides of equation (2), get the equation:
 | | | -3 | A | + | | B | + | | 5 | C | + | | | 7 50 | D | = | | 0 | | (1) |
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Multiply both sides of equation (4) by 5 Divide both sides of equation (4) by 107, get the equation:, then subtract both sides of equation (13) from both sides of equation (1), get the equation:
Multiply both sides of equation (3) by 10 Divide both sides of equation (3) by 3, get the equation:, then add the two sides of equation (14) to both sides of equation (2), get the equation:
Multiply both sides of equation (3) by 5 Divide both sides of equation (3) by 2, get the equation:, then add the two sides of equation (15) to both sides of equation (1), get the equation:
Multiply both sides of equation (2) by 3 Divide both sides of equation (2) by 8, get the equation:, then add the two sides of equation (16) 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》 |