detailed information: The input equation set is:
| | | | 3 | A | + | | B | + | | C | + | | D | | -1 | E | + | | F | = | | 1 | | (1) |
| | A | + | | 3 | B | + | | C | + | | D | + | | E | | -1 | F | = | | 1 | | (2) |
| | A | | -1 | B | + | | 3 | C | + | | D | + | | E | + | | F | = | | 1 | | (3) |
| -1 | A | + | | B | + | | C | + | | 3 | D | + | | E | + | | F | = | | 1 | | (4) |
| | A | + | | B | + | | C | | -1 | D | + | | 3 | E | + | | F | = | | 1 | | (5) |
| | A | + | | B | | -1 | C | + | | D | + | | E | + | | 3 | F | = | | 1 | | (6) |
| Question solving process:
Divide the two sides of equation (1) by 3, the equation can be obtained: | | A | + | | | 1 3 | B | + | | | 1 3 | C | + | | | 1 3 | D | | - | 1 3 | E | + | | | 1 3 | F | = | | | 1 3 | (7) | , then subtract both sides of equation (7) from both sides of equation (2), the equations are reduced to:
| | | | 3 | A | + | | B | + | | C | + | | D | | -1 | E | + | | F | = | | 1 | | (1) |
| | | 8 3 | B | + | | | 2 3 | C | + | | | 2 3 | D | + | | | 4 3 | E | | - | 4 3 | F | = | | | 2 3 | | (2) |
| | A | | -1 | B | + | | 3 | C | + | | D | + | | E | + | | F | = | | 1 | | (3) |
| -1 | A | + | | B | + | | C | + | | 3 | D | + | | E | + | | F | = | | 1 | | (4) |
| | A | + | | B | + | | C | | -1 | D | + | | 3 | E | + | | F | = | | 1 | | (5) |
| | A | + | | B | | -1 | C | + | | D | + | | E | + | | 3 | F | = | | 1 | | (6) |
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Divide the two sides of equation (1) by 3, the equation can be obtained: | | A | + | | | 1 3 | B | + | | | 1 3 | C | + | | | 1 3 | D | | - | 1 3 | E | + | | | 1 3 | F | = | | | 1 3 | (8) | , then subtract both sides of equation (8) from both sides of equation (3), the equations are reduced to:
| | | | 3 | A | + | | B | + | | C | + | | D | | -1 | E | + | | F | = | | 1 | | (1) |
| | | 8 3 | B | + | | | 2 3 | C | + | | | 2 3 | D | + | | | 4 3 | E | | - | 4 3 | F | = | | | 2 3 | | (2) |
| - | 4 3 | B | + | | | 8 3 | C | + | | | 2 3 | D | + | | | 4 3 | E | + | | | 2 3 | F | = | | | 2 3 | | (3) |
| -1 | A | + | | B | + | | C | + | | 3 | D | + | | E | + | | F | = | | 1 | | (4) |
| | A | + | | B | + | | C | | -1 | D | + | | 3 | E | + | | F | = | | 1 | | (5) |
| | A | + | | B | | -1 | C | + | | D | + | | E | + | | 3 | F | = | | 1 | | (6) |
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Divide the two sides of equation (1) by 3, the equation can be obtained: | | A | + | | | 1 3 | B | + | | | 1 3 | C | + | | | 1 3 | D | | - | 1 3 | E | + | | | 1 3 | F | = | | | 1 3 | (9) | , then add the two sides of equation (9) to both sides of equation (4), the equations are reduced to:
| | | | 3 | A | + | | B | + | | C | + | | D | | -1 | E | + | | F | = | | 1 | | (1) |
| | | 8 3 | B | + | | | 2 3 | C | + | | | 2 3 | D | + | | | 4 3 | E | | - | 4 3 | F | = | | | 2 3 | | (2) |
| - | 4 3 | B | + | | | 8 3 | C | + | | | 2 3 | D | + | | | 4 3 | E | + | | | 2 3 | F | = | | | 2 3 | | (3) |
| | | 4 3 | B | + | | | 4 3 | C | + | | | 10 3 | D | + | | | 2 3 | E | + | | | 4 3 | F | = | | | 4 3 | | (4) |
| | A | + | | B | + | | C | | -1 | D | + | | 3 | E | + | | F | = | | 1 | | (5) |
| | A | + | | B | | -1 | C | + | | D | + | | E | + | | 3 | F | = | | 1 | | (6) |
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Divide the two sides of equation (1) by 3, the equation can be obtained: | | A | + | | | 1 3 | B | + | | | 1 3 | C | + | | | 1 3 | D | | - | 1 3 | E | + | | | 1 3 | F | = | | | 1 3 | (10) | , then subtract both sides of equation (10) from both sides of equation (5), the equations are reduced to:
| | | | 3 | A | + | | B | + | | C | + | | D | | -1 | E | + | | F | = | | 1 | | (1) |
| | | 8 3 | B | + | | | 2 3 | C | + | | | 2 3 | D | + | | | 4 3 | E | | - | 4 3 | F | = | | | 2 3 | | (2) |
| - | 4 3 | B | + | | | 8 3 | C | + | | | 2 3 | D | + | | | 4 3 | E | + | | | 2 3 | F | = | | | 2 3 | | (3) |
| | | 4 3 | B | + | | | 4 3 | C | + | | | 10 3 | D | + | | | 2 3 | E | + | | | 4 3 | F | = | | | 4 3 | | (4) |
| | | 2 3 | B | + | | | 2 3 | C | | - | 4 3 | D | + | | | 10 3 | E | + | | | 2 3 | F | = | | | 2 3 | | (5) |
| | A | + | | B | | -1 | C | + | | D | + | | E | + | | 3 | F | = | | 1 | | (6) |
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Divide the two sides of equation (1) by 3, the equation can be obtained: | | A | + | | | 1 3 | B | + | | | 1 3 | C | + | | | 1 3 | D | | - | 1 3 | E | + | | | 1 3 | F | = | | | 1 3 | (11) | , then subtract both sides of equation (11) from both sides of equation (6), the equations are reduced to:
| | | | 3 | A | + | | B | + | | C | + | | D | | -1 | E | + | | F | = | | 1 | | (1) |
| | | 8 3 | B | + | | | 2 3 | C | + | | | 2 3 | D | + | | | 4 3 | E | | - | 4 3 | F | = | | | 2 3 | | (2) |
| - | 4 3 | B | + | | | 8 3 | C | + | | | 2 3 | D | + | | | 4 3 | E | + | | | 2 3 | F | = | | | 2 3 | | (3) |
| | | 4 3 | B | + | | | 4 3 | C | + | | | 10 3 | D | + | | | 2 3 | E | + | | | 4 3 | F | = | | | 4 3 | | (4) |
| | | 2 3 | B | + | | | 2 3 | C | | - | 4 3 | D | + | | | 10 3 | E | + | | | 2 3 | F | = | | | 2 3 | | (5) |
| | | 2 3 | B | | - | 4 3 | C | + | | | 2 3 | D | + | | | 4 3 | E | + | | | 8 3 | F | = | | | 2 3 | | (6) |
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Divide the two sides of equation (2) by 2, the equation can be obtained: | | | 4 3 | B | + | | | 1 3 | C | + | | | 1 3 | D | + | | | 2 3 | E | | - | 2 3 | F | = | | | 1 3 | (12) | , then add the two sides of equation (12) to both sides of equation (3), the equations are reduced to:
| | | | 3 | A | + | | B | + | | C | + | | D | | -1 | E | + | | F | = | | 1 | | (1) |
| | | 8 3 | B | + | | | 2 3 | C | + | | | 2 3 | D | + | | | 4 3 | E | | - | 4 3 | F | = | | | 2 3 | | (2) |
| | | | 4 3 | B | + | | | 4 3 | C | + | | | 10 3 | D | + | | | 2 3 | E | + | | | 4 3 | F | = | | | 4 3 | | (4) |
| | | 2 3 | B | + | | | 2 3 | C | | - | 4 3 | D | + | | | 10 3 | E | + | | | 2 3 | F | = | | | 2 3 | | (5) |
| | | 2 3 | B | | - | 4 3 | C | + | | | 2 3 | D | + | | | 4 3 | E | + | | | 8 3 | F | = | | | 2 3 | | (6) |
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Divide the two sides of equation (2) by 2, the equation can be obtained: | | | 4 3 | B | + | | | 1 3 | C | + | | | 1 3 | D | + | | | 2 3 | E | | - | 2 3 | F | = | | | 1 3 | (13) | , then subtract both sides of equation (13) from both sides of equation (4), the equations are reduced to:
| | | | 3 | A | + | | B | + | | C | + | | D | | -1 | E | + | | F | = | | 1 | | (1) |
| | | 8 3 | B | + | | | 2 3 | C | + | | | 2 3 | D | + | | | 4 3 | E | | - | 4 3 | F | = | | | 2 3 | | (2) |
| | | | | 2 3 | B | + | | | 2 3 | C | | - | 4 3 | D | + | | | 10 3 | E | + | | | 2 3 | F | = | | | 2 3 | | (5) |
| | | 2 3 | B | | - | 4 3 | C | + | | | 2 3 | D | + | | | 4 3 | E | + | | | 8 3 | F | = | | | 2 3 | | (6) |
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Divide the two sides of equation (2) by 4, the equation can be obtained: | | | 2 3 | B | + | | | 1 6 | C | + | | | 1 6 | D | + | | | 1 3 | E | | - | 1 3 | F | = | | | 1 6 | (14) | , then subtract both sides of equation (14) from both sides of equation (5), the equations are reduced to:
| | | | 3 | A | + | | B | + | | C | + | | D | | -1 | E | + | | F | = | | 1 | | (1) |
| | | 8 3 | B | + | | | 2 3 | C | + | | | 2 3 | D | + | | | 4 3 | E | | - | 4 3 | F | = | | | 2 3 | | (2) |
| | | | | 1 2 | C | | - | 3 2 | D | + | | 3 | E | + | | F | = | | | 1 2 | | (5) |
| | | 2 3 | B | | - | 4 3 | C | + | | | 2 3 | D | + | | | 4 3 | E | + | | | 8 3 | F | = | | | 2 3 | | (6) |
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Divide the two sides of equation (2) by 4, the equation can be obtained: | | | 2 3 | B | + | | | 1 6 | C | + | | | 1 6 | D | + | | | 1 3 | E | | - | 1 3 | F | = | | | 1 6 | (15) | , then subtract both sides of equation (15) from both sides of equation (6), the equations are reduced to:
| | | | 3 | A | + | | B | + | | C | + | | D | | -1 | E | + | | F | = | | 1 | | (1) |
| | | 8 3 | B | + | | | 2 3 | C | + | | | 2 3 | D | + | | | 4 3 | E | | - | 4 3 | F | = | | | 2 3 | | (2) |
| | | | | 1 2 | C | | - | 3 2 | D | + | | 3 | E | + | | F | = | | | 1 2 | | (5) |
| - | 3 2 | C | + | | | 1 2 | D | + | | E | + | | 3 | F | = | | | 1 2 | | (6) |
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Divide the two sides of equation (3) by 3, the equation can be obtained: , then subtract both sides of equation (16) from both sides of equation (4), the equations are reduced to:
| | | | 3 | A | + | | B | + | | C | + | | D | | -1 | E | + | | F | = | | 1 | | (1) |
| | | 8 3 | B | + | | | 2 3 | C | + | | | 2 3 | D | + | | | 4 3 | E | | - | 4 3 | F | = | | | 2 3 | | (2) |
| | | | | 1 2 | C | | - | 3 2 | D | + | | 3 | E | + | | F | = | | | 1 2 | | (5) |
| - | 3 2 | C | + | | | 1 2 | D | + | | E | + | | 3 | F | = | | | 1 2 | | (6) |
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Divide the two sides of equation (3) by 6, the equation can be obtained: | | | 1 2 | C | + | | | 1 6 | D | + | | | 1 3 | E | = | | | 1 6 | (17) | , then subtract both sides of equation (17) from both sides of equation (5), the equations are reduced to:
| | | | 3 | A | + | | B | + | | C | + | | D | | -1 | E | + | | F | = | | 1 | | (1) |
| | | 8 3 | B | + | | | 2 3 | C | + | | | 2 3 | D | + | | | 4 3 | E | | - | 4 3 | F | = | | | 2 3 | | (2) |
| | | | - | 3 2 | C | + | | | 1 2 | D | + | | E | + | | 3 | F | = | | | 1 2 | | (6) |
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Divide the two sides of equation (3) by 2, the equation can be obtained: , then add the two sides of equation (18) to both sides of equation (6), the equations are reduced to:
| | | | 3 | A | + | | B | + | | C | + | | D | | -1 | E | + | | F | = | | 1 | | (1) |
| | | 8 3 | B | + | | | 2 3 | C | + | | | 2 3 | D | + | | | 4 3 | E | | - | 4 3 | F | = | | | 2 3 | | (2) |
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Multiply both sides of equation (4) by 5 Divide the two sides of equation (4) by 8, the equation can be obtained: | | | 5 3 | D | | - | 5 12 | E | + | | | 5 4 | F | = | | | 5 12 | (19) | , then add the two sides of equation (19) to both sides of equation (5), the equations are reduced to:
| | | | 3 | A | + | | B | + | | C | + | | D | | -1 | E | + | | F | = | | 1 | | (1) |
| | | 8 3 | B | + | | | 2 3 | C | + | | | 2 3 | D | + | | | 4 3 | E | | - | 4 3 | F | = | | | 2 3 | | (2) |
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Multiply both sides of equation (4) by 3 Divide the two sides of equation (4) by 8, the equation can be obtained: , then subtract both sides of equation (20) from both sides of equation (6), the equations are reduced to:
| | | | 3 | A | + | | B | + | | C | + | | D | | -1 | E | + | | F | = | | 1 | | (1) |
| | | 8 3 | B | + | | | 2 3 | C | + | | | 2 3 | D | + | | | 4 3 | E | | - | 4 3 | F | = | | | 2 3 | | (2) |
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Subtract both sides of equation (5) from both sides of equation (6) ,the equations are reduced to:
| | | | 3 | A | + | | B | + | | C | + | | D | | -1 | E | + | | F | = | | 1 | | (1) |
| | | 8 3 | B | + | | | 2 3 | C | + | | | 2 3 | D | + | | | 4 3 | E | | - | 4 3 | F | = | | | 2 3 | | (2) |
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Multiply both sides of equation (5) by 8 Divide both sides of equation (5) by 27, get the equation:, then add the two sides of equation (21) to both sides of equation (4), get the equation:
| | | | 3 | A | + | | B | + | | C | + | | D | | -1 | E | + | | F | = | | 1 | | (1) |
| | | 8 3 | B | + | | | 2 3 | C | + | | | 2 3 | D | + | | | 4 3 | E | | - | 4 3 | F | = | | | 2 3 | | (2) |
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Multiply both sides of equation (5) by 8 Divide both sides of equation (5) by 9, get the equation:, then subtract both sides of equation (22) from both sides of equation (3), get the equation:
| | | | 3 | A | + | | B | + | | C | + | | D | | -1 | E | + | | F | = | | 1 | | (1) |
| | | 8 3 | B | + | | | 2 3 | C | + | | | 2 3 | D | + | | | 4 3 | E | | - | 4 3 | F | = | | | 2 3 | | (2) |
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Multiply both sides of equation (5) by 16 Divide both sides of equation (5) by 27, get the equation:, then subtract both sides of equation (23) from both sides of equation (2), get the equation:
| | | | 3 | A | + | | B | + | | C | + | | D | | -1 | E | + | | F | = | | 1 | | (1) |
| | | 8 3 | B | + | | | 2 3 | C | + | | | 2 3 | D | | - | 8 3 | F | = | | | 2 9 | | (2) |
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Multiply both sides of equation (5) by 4 Divide both sides of equation (5) by 9, get the equation:, then add the two sides of equation (24) to both sides of equation (1), get the equation:
| | | | 3 | A | + | | B | + | | C | + | | D | + | | 2 | F | = | | | 4 3 | | (1) |
| | | 8 3 | B | + | | | 2 3 | C | + | | | 2 3 | D | | - | 8 3 | F | = | | | 2 9 | | (2) |
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Multiply both sides of equation (4) by 3 Divide both sides of equation (4) by 8, get the equation:, then subtract both sides of equation (25) from both sides of equation (3), get the equation:
| | | | 3 | A | + | | B | + | | C | + | | D | + | | 2 | F | = | | | 4 3 | | (1) |
| | | 8 3 | B | + | | | 2 3 | C | + | | | 2 3 | D | | - | 8 3 | F | = | | | 2 9 | | (2) |
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Divide both sides of equation (4) by 4, get the equation:, then subtract both sides of equation (26) from both sides of equation (2), get the equation:
| | | | 3 | A | + | | B | + | | C | + | | D | + | | 2 | F | = | | | 4 3 | | (1) |
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Multiply both sides of equation (4) by 3 Divide both sides of equation (4) by 8, get the equation:, then subtract both sides of equation (27) from both sides of equation (1), get the equation:
Multiply both sides of equation (3) by 2 Divide both sides of equation (3) by 9, get the equation:, then subtract both sides of equation (28) from both sides of equation (2), get the equation:
Divide both sides of equation (3) by 3, get the equation:, then subtract both sides of equation (29) from 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 subtract both sides of equation (30) 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:
Where: F 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》 |