detailed information: The input equation set is:
| | | | -1 | A | + | | 3 | B | | -1 | C | | -1 | E | = | | 2000 | | (2) |
| | | | Question solving process:
Divide the two sides of equation (1) by 2, the equation can be obtained: | | A | | - | 1 2 | B | | - | 1 2 | D | = | | -6000 | (6) | , then add the two sides of equation (6) to both sides of equation (2), the equations are reduced to:
| | | | | | 5 2 | B | | -1 | C | | - | 1 2 | D | | -1 | E | = | | -4000 | | (2) |
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Divide the two sides of equation (1) by 2, the equation can be obtained: | | A | | - | 1 2 | B | | - | 1 2 | D | = | | -6000 | (7) | , then add the two sides of equation (7) to both sides of equation (4), the equations are reduced to:
| | | | | | 5 2 | B | | -1 | C | | - | 1 2 | D | | -1 | E | = | | -4000 | | (2) |
| | - | 1 2 | B | + | | | 3 2 | D | | -1 | E | = | | -4000 | | (4) |
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Multiply both sides of equation (2) by 4 Divide the two sides of equation (2) by 5, the equation can be obtained: | | 2 | B | | - | 4 5 | C | | - | 2 5 | D | | - | 4 5 | E | = | | -3200 | (8) | , then add the two sides of equation (8) to both sides of equation (3), the equations are reduced to:
| | | | | | 5 2 | B | | -1 | C | | - | 1 2 | D | | -1 | E | = | | -4000 | | (2) |
| | | 6 5 | C | | - | 2 5 | D | | - | 4 5 | E | = | | -1200 | | (3) |
| - | 1 2 | B | + | | | 3 2 | D | | -1 | E | = | | -4000 | | (4) |
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Divide the two sides of equation (2) by 5, the equation can be obtained: | | | 1 2 | B | | - | 1 5 | C | | - | 1 10 | D | | - | 1 5 | E | = | | -800 | (9) | , then add the two sides of equation (9) to both sides of equation (4), the equations are reduced to:
| | | | | | 5 2 | B | | -1 | C | | - | 1 2 | D | | -1 | E | = | | -4000 | | (2) |
| | | 6 5 | C | | - | 2 5 | D | | - | 4 5 | E | = | | -1200 | | (3) |
| - | 1 5 | C | + | | | 7 5 | D | | - | 6 5 | E | = | | -4800 | | (4) |
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Multiply both sides of equation (2) by 2 Divide the two sides of equation (2) by 5, the equation can be obtained: | | B | | - | 2 5 | C | | - | 1 5 | D | | - | 2 5 | E | = | | -1600 | (10) | , then add the two sides of equation (10) to both sides of equation (5), the equations are reduced to:
| | | | | | 5 2 | B | | -1 | C | | - | 1 2 | D | | -1 | E | = | | -4000 | | (2) |
| | | 6 5 | C | | - | 2 5 | D | | - | 4 5 | E | = | | -1200 | | (3) |
| - | 1 5 | C | + | | | 7 5 | D | | - | 6 5 | E | = | | -4800 | | (4) |
| - | 2 5 | C | | - | 6 5 | D | + | | | 13 5 | E | = | | 400 | | (5) |
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Divide the two sides of equation (3) by 6, the equation can be obtained: | | | 1 5 | C | | - | 1 15 | D | | - | 2 15 | E | = | | -200 | (11) | , then add the two sides of equation (11) to both sides of equation (4), the equations are reduced to:
| | | | | | 5 2 | B | | -1 | C | | - | 1 2 | D | | -1 | E | = | | -4000 | | (2) |
| | | 6 5 | C | | - | 2 5 | D | | - | 4 5 | E | = | | -1200 | | (3) |
| | - | 2 5 | C | | - | 6 5 | D | + | | | 13 5 | E | = | | 400 | | (5) |
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Divide the two sides of equation (3) by 3, the equation can be obtained: | | | 2 5 | C | | - | 2 15 | D | | - | 4 15 | E | = | | -400 | (12) | , then add the two sides of equation (12) to both sides of equation (5), the equations are reduced to:
| | | | | | 5 2 | B | | -1 | C | | - | 1 2 | D | | -1 | E | = | | -4000 | | (2) |
| | | 6 5 | C | | - | 2 5 | D | | - | 4 5 | E | = | | -1200 | | (3) |
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Add both sides of equation (4) to both sides of equation (5) ,the equations are reduced to:
| | | | | | 5 2 | B | | -1 | C | | - | 1 2 | D | | -1 | E | = | | -4000 | | (2) |
| | | 6 5 | C | | - | 2 5 | D | | - | 4 5 | E | = | | -1200 | | (3) |
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Multiply both sides of equation (5) by 4 Divide both sides of equation (5) by 3, get the equation:, then add the two sides of equation (13) to both sides of equation (4), get the equation:
| | | | | | 5 2 | B | | -1 | C | | - | 1 2 | D | | -1 | E | = | | -4000 | | (2) |
| | | 6 5 | C | | - | 2 5 | D | | - | 4 5 | E | = | | -1200 | | (3) |
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Multiply both sides of equation (5) by 4 Divide both sides of equation (5) by 5, get the equation:, then add the two sides of equation (14) to both sides of equation (3), get the equation:
| | | | | | 5 2 | B | | -1 | C | | - | 1 2 | D | | -1 | E | = | | -4000 | | (2) |
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Add both sides of equation (5) to both sides of equation (2), get the equation:
| | | | | | 5 2 | B | | -1 | C | | - | 1 2 | D | = | | -9000 | | (2) |
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Multiply both sides of equation (4) by 3 Divide both sides of equation (4) by 10, get the equation:, then add the two sides of equation (15) to both sides of equation (3), get the equation:
| | | | | | 5 2 | B | | -1 | C | | - | 1 2 | D | = | | -9000 | | (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 add the two sides of equation (16) to both sides of equation (2), get the equation:
Multiply both sides of equation (4) by 3 Divide both sides of equation (4) by 4, get the equation:, then add the two sides of equation (17) to both sides of equation (1), get the equation:
Multiply both sides of equation (3) by 5 Divide both sides of equation (3) by 6, get the equation:, then add the two sides of equation (18) to both sides of equation (2), get the equation:
Multiply both sides of equation (2) by 2 Divide both sides of equation (2) by 5, get the equation:, then add the two sides of equation (19) 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》 |