detailed information: The input equation set is:
| | | | A | + | | B | + | | C | + | | D | + | | E | + | | F | + | | G | + | | H | + | | I | = | | 45 | | (1) |
| | | | | | | | | Question solving process:
Subtract both sides of equation (1) from both sides of equation (2) ,the equations are reduced to:
| | | | A | + | | B | + | | C | + | | D | + | | E | + | | F | + | | G | + | | H | + | | I | = | | 45 | | (1) |
| -1 | D | | -1 | E | | -1 | F | | -1 | G | | -1 | H | | -1 | I | = | | -30 | | (2) |
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Subtract both sides of equation (1) from both sides of equation (5) ,the equations are reduced to:
| | | | A | + | | B | + | | C | + | | D | + | | E | + | | F | + | | G | + | | H | + | | I | = | | 45 | | (1) |
| -1 | D | | -1 | E | | -1 | F | | -1 | G | | -1 | H | | -1 | I | = | | -30 | | (2) |
| | | -1 | B | | -1 | C | | -1 | E | | -1 | F | | -1 | H | | -1 | I | = | | -30 | | (5) |
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Subtract both sides of equation (1) from both sides of equation (9) ,the equations are reduced to:
| | | | A | + | | B | + | | C | + | | D | + | | E | + | | F | + | | G | + | | H | + | | I | = | | 45 | | (1) |
| -1 | D | | -1 | E | | -1 | F | | -1 | G | | -1 | H | | -1 | I | = | | -30 | | (2) |
| | | -1 | B | | -1 | C | | -1 | E | | -1 | F | | -1 | H | | -1 | I | = | | -30 | | (5) |
| | | | -1 | B | | -1 | C | | -1 | D | | -1 | F | | -1 | G | | -1 | H | = | | -30 | | (9) |
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交After the exchange of equation (2) and equation (5), the equation system becomes:
| | | | A | + | | B | + | | C | + | | D | + | | E | + | | F | + | | G | + | | H | + | | I | = | | 45 | | (1) |
| -1 | B | | -1 | C | | -1 | E | | -1 | F | | -1 | H | | -1 | I | = | | -30 | | (2) |
| | | -1 | D | | -1 | E | | -1 | F | | -1 | G | | -1 | H | | -1 | I | = | | -30 | | (5) |
| | | | -1 | B | | -1 | C | | -1 | D | | -1 | F | | -1 | G | | -1 | H | = | | -30 | | (9) |
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Add both sides of equation (2) to both sides of equation (6) ,the equations are reduced to:
| | | | A | + | | B | + | | C | + | | D | + | | E | + | | F | + | | G | + | | H | + | | I | = | | 45 | | (1) |
| -1 | B | | -1 | C | | -1 | E | | -1 | F | | -1 | H | | -1 | I | = | | -30 | | (2) |
| | | -1 | D | | -1 | E | | -1 | F | | -1 | G | | -1 | H | | -1 | I | = | | -30 | | (5) |
| | | | -1 | B | | -1 | C | | -1 | D | | -1 | F | | -1 | G | | -1 | H | = | | -30 | | (9) |
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Subtract both sides of equation (2) from both sides of equation (9) ,the equations are reduced to:
| | | | A | + | | B | + | | C | + | | D | + | | E | + | | F | + | | G | + | | H | + | | I | = | | 45 | | (1) |
| -1 | B | | -1 | C | | -1 | E | | -1 | F | | -1 | H | | -1 | I | = | | -30 | | (2) |
| | | -1 | D | | -1 | E | | -1 | F | | -1 | G | | -1 | H | | -1 | I | = | | -30 | | (5) |
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交After the exchange of equation (3) and equation (6), the equation system becomes:
| | | | A | + | | B | + | | C | + | | D | + | | E | + | | F | + | | G | + | | H | + | | I | = | | 45 | | (1) |
| -1 | B | | -1 | C | | -1 | E | | -1 | F | | -1 | H | | -1 | I | = | | -30 | | (2) |
| | | -1 | D | | -1 | E | | -1 | F | | -1 | G | | -1 | H | | -1 | I | = | | -30 | | (5) |
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Add both sides of equation (3) to both sides of equation (7) ,the equations are reduced to:
| | | | A | + | | B | + | | C | + | | D | + | | E | + | | F | + | | G | + | | H | + | | I | = | | 45 | | (1) |
| -1 | B | | -1 | C | | -1 | E | | -1 | F | | -1 | H | | -1 | I | = | | -30 | | (2) |
| | | -1 | D | | -1 | E | | -1 | F | | -1 | G | | -1 | H | | -1 | I | = | | -30 | | (5) |
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Add both sides of equation (3) to both sides of equation (8) ,the equations are reduced to:
| | | | A | + | | B | + | | C | + | | D | + | | E | + | | F | + | | G | + | | H | + | | I | = | | 45 | | (1) |
| -1 | B | | -1 | C | | -1 | E | | -1 | F | | -1 | H | | -1 | I | = | | -30 | | (2) |
| | | -1 | D | | -1 | E | | -1 | F | | -1 | G | | -1 | H | | -1 | I | = | | -30 | | (5) |
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交After the exchange of equation (4) and equation (5), the equation system becomes:
| | | | A | + | | B | + | | C | + | | D | + | | E | + | | F | + | | G | + | | H | + | | I | = | | 45 | | (1) |
| -1 | B | | -1 | C | | -1 | E | | -1 | F | | -1 | H | | -1 | I | = | | -30 | | (2) |
| | -1 | D | | -1 | E | | -1 | F | | -1 | G | | -1 | H | | -1 | I | = | | -30 | | (4) |
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Add both sides of equation (4) to both sides of equation (6) ,the equations are reduced to:
| | | | A | + | | B | + | | C | + | | D | + | | E | + | | F | + | | G | + | | H | + | | I | = | | 45 | | (1) |
| -1 | B | | -1 | C | | -1 | E | | -1 | F | | -1 | H | | -1 | I | = | | -30 | | (2) |
| | -1 | D | | -1 | E | | -1 | F | | -1 | G | | -1 | H | | -1 | I | = | | -30 | | (4) |
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Subtract both sides of equation (4) from both sides of equation (9) ,the equations are reduced to:
| | | | A | + | | B | + | | C | + | | D | + | | E | + | | F | + | | G | + | | H | + | | I | = | | 45 | | (1) |
| -1 | B | | -1 | C | | -1 | E | | -1 | F | | -1 | H | | -1 | I | = | | -30 | | (2) |
| | -1 | D | | -1 | E | | -1 | F | | -1 | G | | -1 | H | | -1 | I | = | | -30 | | (4) |
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交After the exchange of equation (5) and equation (8), the equation system becomes:
| | | | A | + | | B | + | | C | + | | D | + | | E | + | | F | + | | G | + | | H | + | | I | = | | 45 | | (1) |
| -1 | B | | -1 | C | | -1 | E | | -1 | F | | -1 | H | | -1 | I | = | | -30 | | (2) |
| | -1 | D | | -1 | E | | -1 | F | | -1 | G | | -1 | H | | -1 | I | = | | -30 | | (4) |
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Multiply both sides of equation (5) by 2, the equation can be obtained: , then subtract both sides of equation (10) from both sides of equation (9), the equations are reduced to:
| | | | A | + | | B | + | | C | + | | D | + | | E | + | | F | + | | G | + | | H | + | | I | = | | 45 | | (1) |
| -1 | B | | -1 | C | | -1 | E | | -1 | F | | -1 | H | | -1 | I | = | | -30 | | (2) |
| | -1 | D | | -1 | E | | -1 | F | | -1 | G | | -1 | H | | -1 | I | = | | -30 | | (4) |
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交After the exchange of equation (6) and equation (9), the equation system becomes:
| | | | A | + | | B | + | | C | + | | D | + | | E | + | | F | + | | G | + | | H | + | | I | = | | 45 | | (1) |
| -1 | B | | -1 | C | | -1 | E | | -1 | F | | -1 | H | | -1 | I | = | | -30 | | (2) |
| | -1 | D | | -1 | E | | -1 | F | | -1 | G | | -1 | H | | -1 | I | = | | -30 | | (4) |
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交After the exchange of equation (7) and equation (8), the equation system becomes:
| | | | A | + | | B | + | | C | + | | D | + | | E | + | | F | + | | G | + | | H | + | | I | = | | 45 | | (1) |
| -1 | B | | -1 | C | | -1 | E | | -1 | F | | -1 | H | | -1 | I | = | | -30 | | (2) |
| | -1 | D | | -1 | E | | -1 | F | | -1 | G | | -1 | H | | -1 | I | = | | -30 | | (4) |
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Add both sides of equation (7) to both sides of equation (9) ,the equations are reduced to:
| | | | A | + | | B | + | | C | + | | D | + | | E | + | | F | + | | G | + | | H | + | | I | = | | 45 | | (1) |
| -1 | B | | -1 | C | | -1 | E | | -1 | F | | -1 | H | | -1 | I | = | | -30 | | (2) |
| | -1 | D | | -1 | E | | -1 | F | | -1 | G | | -1 | H | | -1 | I | = | | -30 | | (4) |
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Multiply both sides of equation (7) by 2, get the equation:, then add the two sides of equation (11) to both sides of equation (6), get the equation:
| | | | A | + | | B | + | | C | + | | D | + | | E | + | | F | + | | G | + | | H | + | | I | = | | 45 | | (1) |
| -1 | B | | -1 | C | | -1 | E | | -1 | F | | -1 | H | | -1 | I | = | | -30 | | (2) |
| | -1 | D | | -1 | E | | -1 | F | | -1 | G | | -1 | H | | -1 | I | = | | -30 | | (4) |
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Subtract both sides of equation (7) from both sides of equation (5), get the equation:
| | | | A | + | | B | + | | C | + | | D | + | | E | + | | F | + | | G | + | | H | + | | I | = | | 45 | | (1) |
| -1 | B | | -1 | C | | -1 | E | | -1 | F | | -1 | H | | -1 | I | = | | -30 | | (2) |
| | -1 | D | | -1 | E | | -1 | F | | -1 | G | | -1 | H | | -1 | I | = | | -30 | | (4) |
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Add both sides of equation (7) to both sides of equation (4), get the equation:
| | | | A | + | | B | + | | C | + | | D | + | | E | + | | F | + | | G | + | | H | + | | I | = | | 45 | | (1) |
| -1 | B | | -1 | C | | -1 | E | | -1 | F | | -1 | H | | -1 | I | = | | -30 | | (2) |
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Subtract both sides of equation (7) from both sides of equation (1), get the equation:
| | | | A | + | | B | + | | C | + | | D | + | | E | + | | F | = | | 30 | | (1) |
| -1 | B | | -1 | C | | -1 | E | | -1 | F | | -1 | H | | -1 | I | = | | -30 | | (2) |
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Divide both sides of equation (6) by 3, get the equation:, then add the two sides of equation (12) to both sides of equation (5), get the equation:
| | | | A | + | | B | + | | C | + | | D | + | | E | + | | F | = | | 30 | | (1) |
| -1 | B | | -1 | C | | -1 | E | | -1 | F | | -1 | H | | -1 | I | = | | -30 | | (2) |
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Divide both sides of equation (6) by 3, get the equation:, then add the two sides of equation (13) to both sides of equation (4), get the equation:
| | | | A | + | | B | + | | C | + | | D | + | | E | + | | F | = | | 30 | | (1) |
| -1 | B | | -1 | C | | -1 | E | | -1 | F | | -1 | H | | -1 | I | = | | -30 | | (2) |
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Divide both sides of equation (6) by 3, get the equation:, then add the two sides of equation (14) to both sides of equation (3), get the equation:
| | | | A | + | | B | + | | C | + | | D | + | | E | + | | F | = | | 30 | | (1) |
| -1 | B | | -1 | C | | -1 | E | | -1 | F | | -1 | H | | -1 | I | = | | -30 | | (2) |
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Divide both sides of equation (6) by 3, get the equation:, then add the two sides of equation (15) to both sides of equation (2), get the equation:
| | | | A | + | | B | + | | C | + | | D | + | | E | + | | F | = | | 30 | | (1) |
| -1 | B | | -1 | C | | -1 | E | + | | I | = | | -10 | | (2) |
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Divide both sides of equation (6) by 3, get the equation:, then subtract both sides of equation (16) from both sides of equation (1), get the equation:
| | | | A | + | | B | + | | C | + | | D | + | | E | | -1 | H | | -2 | I | = | | 10 | | (1) |
| -1 | B | | -1 | C | | -1 | E | + | | I | = | | -10 | | (2) |
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Add both sides of equation (5) to both sides of equation (4), get the equation:
| | | | A | + | | B | + | | C | + | | D | + | | E | | -1 | H | | -2 | I | = | | 10 | | (1) |
| -1 | B | | -1 | C | | -1 | E | + | | I | = | | -10 | | (2) |
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Add both sides of equation (5) to both sides of equation (2), get the equation:
| | | | A | + | | B | + | | C | + | | D | + | | E | | -1 | H | | -2 | I | = | | 10 | | (1) |
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Subtract both sides of equation (5) from both sides of equation (1), get the equation:
| | | | A | + | | B | + | | C | + | | D | | -1 | H | | -2 | I | = | | 5 | | (1) |
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Add both sides of equation (4) to both sides of equation (1), get the equation:
Subtract both sides of equation (3) from both sides of equation (2), get the equation:
Add both sides of equation (3) to both sides of equation (1), get the equation:
Add both sides of equation (2) 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:
Where: H, I are arbitrary constants. 解方程组的详细方法请参阅:《多元一次方程组的解法》 |