detailed information: The input equation set is:
| | | | | 2 | A | | -1 | B | + | | C | + | | 3 | D | + | | 4 | E | = | | -7 | | (2) |
| | 2 | A | | -1 | B | + | | 2 | C | + | | D | | -2 | E | = | | -4 | | (3) |
| | 2 | A | | -3 | B | + | | C | + | | 2 | D | | -2 | E | = | | -9 | | (4) |
| | Question solving process:
Multiply both sides of equation (1) by 2, the equation can be obtained: | | 2 | A | + | | 4 | B | + | | 2 | C | | -2 | D | = | | 12 | (6) | , then subtract both sides of equation (6) from both sides of equation (2), the equations are reduced to:
| | | | -5 | B | | -1 | C | + | | 5 | D | + | | 4 | E | = | | -19 | | (2) |
| | 2 | A | | -1 | B | + | | 2 | C | + | | D | | -2 | E | = | | -4 | | (3) |
| | 2 | A | | -3 | B | + | | C | + | | 2 | D | | -2 | E | = | | -9 | | (4) |
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Multiply both sides of equation (1) by 2, the equation can be obtained: | | 2 | A | + | | 4 | B | + | | 2 | C | | -2 | D | = | | 12 | (7) | , then subtract both sides of equation (7) from both sides of equation (3), the equations are reduced to:
| | | | -5 | B | | -1 | C | + | | 5 | D | + | | 4 | E | = | | -19 | | (2) |
| | | 2 | A | | -3 | B | + | | C | + | | 2 | D | | -2 | E | = | | -9 | | (4) |
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Multiply both sides of equation (1) by 2, the equation can be obtained: | | 2 | A | + | | 4 | B | + | | 2 | C | | -2 | D | = | | 12 | (8) | , then subtract both sides of equation (8) from both sides of equation (4), the equations are reduced to:
| | | | -5 | B | | -1 | C | + | | 5 | D | + | | 4 | E | = | | -19 | | (2) |
| | -7 | B | | -1 | C | + | | 4 | D | | -2 | E | = | | -21 | | (4) |
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Subtract both sides of equation (1) from both sides of equation (5) ,the equations are reduced to:
| | | | -5 | B | | -1 | C | + | | 5 | D | + | | 4 | E | = | | -19 | | (2) |
| | -7 | B | | -1 | C | + | | 4 | D | | -2 | E | = | | -21 | | (4) |
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Subtract both sides of equation (2) from both sides of equation (3) ,the equations are reduced to:
| | | | -5 | B | | -1 | C | + | | 5 | D | + | | 4 | E | = | | -19 | | (2) |
| | -7 | B | | -1 | C | + | | 4 | D | | -2 | E | = | | -21 | | (4) |
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Multiply both sides of equation (2) by 7 Divide the two sides of equation (2) by 5, the equation can be obtained: | -7 | B | | - | 7 5 | C | + | | 7 | D | + | | | 28 5 | E | = | | - | 133 5 | (9) | , then subtract both sides of equation (9) from both sides of equation (4), the equations are reduced to:
| | | | -5 | B | | -1 | C | + | | 5 | D | + | | 4 | E | = | | -19 | | (2) |
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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: | -2 | B | | - | 2 5 | C | + | | 2 | D | + | | | 8 5 | E | = | | - | 38 5 | (10) | , then subtract both sides of equation (10) from both sides of equation (5), the equations are reduced to:
| | | | -5 | B | | -1 | C | + | | 5 | D | + | | 4 | E | = | | -19 | | (2) |
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Multiply both sides of equation (3) by 2 Divide the two sides of equation (3) by 5, the equation can be obtained: | | | 2 5 | C | | - | 4 5 | D | | - | 12 5 | E | = | | | 6 5 | (11) | , then subtract both sides of equation (11) from both sides of equation (4), the equations are reduced to:
| | | | -5 | B | | -1 | C | + | | 5 | D | + | | 4 | E | = | | -19 | | (2) |
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Multiply both sides of equation (3) by 2 Divide the two sides of equation (3) by 5, the equation can be obtained: | | | 2 5 | C | | - | 4 5 | D | | - | 12 5 | E | = | | | 6 5 | (12) | , then subtract both sides of equation (12) from both sides of equation (5), the equations are reduced to:
| | | | -5 | B | | -1 | C | + | | 5 | D | + | | 4 | E | = | | -19 | | (2) |
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Subtract both sides of equation (4) from both sides of equation (5) ,the equations are reduced to:
| | | | -5 | B | | -1 | C | + | | 5 | D | + | | 4 | E | = | | -19 | | (2) |
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Multiply both sides of equation (4) by 10 Divide both sides of equation (4) by 11, get the equation:, then subtract both sides of equation (13) from both sides of equation (3), get the equation:
| | | | -5 | B | | -1 | C | + | | 5 | D | + | | 4 | E | = | | -19 | | (2) |
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Multiply both sides of equation (4) by 25 Divide both sides of equation (4) by 11, 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 (4) by 5 Divide both sides of equation (4) by 11, get the equation:, then subtract both sides of equation (15) from both sides of equation (1), get the equation:
| | | | A | + | | 2 | B | + | | C | + | | | 26 11 | E | = | | 4 | | (1) |
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Add both sides of equation (3) to both sides of equation (2), get the equation:
| | | | A | + | | 2 | B | + | | C | + | | | 26 11 | E | = | | 4 | | (1) |
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Subtract both sides of equation (3) from both sides of equation (1), 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 (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:
Where: E 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》 |