detailed information: The input equation set is:
| | | | A | + | | B | + | | C | + | | D | + | | E | + | | F | = | | 1 | | (1) |
| | | | | | Question solving process:
Divide the two sides of equation (1) by 2, the equation can be obtained: | | | 1 2 | A | + | | | 1 2 | B | + | | | 1 2 | C | + | | | 1 2 | D | + | | | 1 2 | E | + | | | 1 2 | F | = | | | 1 2 | (7) | , then subtract both sides of equation (7) from both sides of equation (2), the equations are reduced to:
| | | | A | + | | B | + | | C | + | | D | + | | E | + | | F | = | | 1 | | (1) |
| -1 | B | | - | 1 2 | D | | - | 1 2 | E | | - | 1 2 | F | = | | - | 1 2 | | (2) |
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Divide the two sides of equation (2) by 2, the equation can be obtained: | - | 1 2 | B | | - | 1 4 | D | | - | 1 4 | E | | - | 1 4 | F | = | | - | 1 4 | (8) | , then add the two sides of equation (8) to both sides of equation (3), the equations are reduced to:
| | | | A | + | | B | + | | C | + | | D | + | | E | + | | F | = | | 1 | | (1) |
| -1 | B | | - | 1 2 | D | | - | 1 2 | E | | - | 1 2 | F | = | | - | 1 2 | | (2) |
| - | 3 5 | C | + | | | 7 20 | D | | - | 1 4 | E | | - | 1 4 | F | = | | - | 1 4 | | (3) |
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Add both sides of equation (3) to both sides of equation (4) ,the equations are reduced to:
| | | | A | + | | B | + | | C | + | | D | + | | E | + | | F | = | | 1 | | (1) |
| -1 | B | | - | 1 2 | D | | - | 1 2 | E | | - | 1 2 | F | = | | - | 1 2 | | (2) |
| - | 3 5 | C | + | | | 7 20 | D | | - | 1 4 | E | | - | 1 4 | F | = | | - | 1 4 | | (3) |
| - | 1 4 | D | + | | | 7 20 | E | | - | 1 4 | F | = | | - | 1 4 | | (4) |
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Multiply both sides of equation (4) by 12 Divide the two sides of equation (4) by 5, the equation can be obtained: | - | 3 5 | D | + | | | 21 25 | E | | - | 3 5 | F | = | | - | 3 5 | (9) | , then add the two sides of equation (9) to both sides of equation (5), the equations are reduced to:
| | | | A | + | | B | + | | C | + | | D | + | | E | + | | F | = | | 1 | | (1) |
| -1 | B | | - | 1 2 | D | | - | 1 2 | E | | - | 1 2 | F | = | | - | 1 2 | | (2) |
| - | 3 5 | C | + | | | 7 20 | D | | - | 1 4 | E | | - | 1 4 | F | = | | - | 1 4 | | (3) |
| - | 1 4 | D | + | | | 7 20 | E | | - | 1 4 | F | = | | - | 1 4 | | (4) |
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Multiply both sides of equation (5) by 5 Divide the two sides of equation (5) by 2, the equation can be obtained: , then subtract both sides of equation (10) from both sides of equation (6), the equations are reduced to:
| | | | A | + | | B | + | | C | + | | D | + | | E | + | | F | = | | 1 | | (1) |
| -1 | B | | - | 1 2 | D | | - | 1 2 | E | | - | 1 2 | F | = | | - | 1 2 | | (2) |
| - | 3 5 | C | + | | | 7 20 | D | | - | 1 4 | E | | - | 1 4 | F | = | | - | 1 4 | | (3) |
| - | 1 4 | D | + | | | 7 20 | E | | - | 1 4 | F | = | | - | 1 4 | | (4) |
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Multiply both sides of equation (6) by 5 Divide both sides of equation (6) by 12, get the equation:, then subtract both sides of equation (11) from both sides of equation (4), get the equation:
| | | | A | + | | B | + | | C | + | | D | + | | E | + | | F | = | | 1 | | (1) |
| -1 | B | | - | 1 2 | D | | - | 1 2 | E | | - | 1 2 | F | = | | - | 1 2 | | (2) |
| - | 3 5 | C | + | | | 7 20 | D | | - | 1 4 | E | | - | 1 4 | F | = | | - | 1 4 | | (3) |
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Multiply both sides of equation (6) by 5 Divide both sides of equation (6) by 12, get the equation:, then subtract both sides of equation (12) from both sides of equation (3), get the equation:
| | | | A | + | | B | + | | C | + | | D | + | | E | + | | F | = | | 1 | | (1) |
| -1 | B | | - | 1 2 | D | | - | 1 2 | E | | - | 1 2 | F | = | | - | 1 2 | | (2) |
| - | 3 5 | C | + | | | 7 20 | D | | - | 1 4 | E | = | | - | 7 8 | | (3) |
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Multiply both sides of equation (6) by 5 Divide both sides of equation (6) by 6, get the equation:, then subtract both sides of equation (13) from both sides of equation (2), get the equation:
| | | | A | + | | B | + | | C | + | | D | + | | E | + | | F | = | | 1 | | (1) |
| -1 | B | | - | 1 2 | D | | - | 1 2 | E | = | | - | 7 4 | | (2) |
| - | 3 5 | C | + | | | 7 20 | D | | - | 1 4 | E | = | | - | 7 8 | | (3) |
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Multiply both sides of equation (6) by 5 Divide both sides of equation (6) by 3, get the equation:, then add the two sides of equation (14) to both sides of equation (1), get the equation:
| | | | A | + | | B | + | | C | + | | D | + | | E | = | | | 7 2 | | (1) |
| -1 | B | | - | 1 2 | D | | - | 1 2 | E | = | | - | 7 4 | | (2) |
| - | 3 5 | C | + | | | 7 20 | D | | - | 1 4 | E | = | | - | 7 8 | | (3) |
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Multiply both sides of equation (5) by 35 Divide both sides of equation (5) by 24, get the equation:, then subtract both sides of equation (15) from both sides of equation (4), get the equation:
| | | | A | + | | B | + | | C | + | | D | + | | E | = | | | 7 2 | | (1) |
| -1 | B | | - | 1 2 | D | | - | 1 2 | E | = | | - | 7 4 | | (2) |
| - | 3 5 | C | + | | | 7 20 | D | | - | 1 4 | E | = | | - | 7 8 | | (3) |
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Multiply both sides of equation (5) by 25 Divide both sides of equation (5) by 24, get the equation:, then add the two sides of equation (16) to both sides of equation (3), get the equation:
| | | | A | + | | B | + | | C | + | | D | + | | E | = | | | 7 2 | | (1) |
| -1 | B | | - | 1 2 | D | | - | 1 2 | E | = | | - | 7 4 | | (2) |
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Multiply both sides of equation (5) by 25 Divide both sides of equation (5) by 12, get the equation:, then add the two sides of equation (17) to both sides of equation (2), get the equation:
| | | | A | + | | B | + | | C | + | | D | + | | E | = | | | 7 2 | | (1) |
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Multiply both sides of equation (5) by 25 Divide both sides of equation (5) by 6, get the equation:, then subtract both sides of equation (18) from both sides of equation (1), get the equation:
Multiply both sides of equation (4) by 7 Divide both sides of equation (4) by 5, get the equation:, then add the two sides of equation (19) to both sides of equation (3), get the equation:
Multiply both sides of equation (4) by 2, get the equation:, then subtract both sides of equation (20) from both sides of equation (2), get the equation:
Multiply both sides of equation (4) by 4, get the equation:, then add the two sides of equation (21) to both sides of equation (1), get the equation:
Multiply both sides of equation (3) by 5 Divide both sides of equation (3) by 3, get the equation:, then add the two sides of equation (22) 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:
Convert the solution of the equation set to decimals:
解方程组的详细方法请参阅:《多元一次方程组的解法》 |