detailed information: The input equation set is:
| | | | A | + | | B | + | | 2 | C | + | | 3 | D | + | | 5 | E | = | | 0 | | (1) |
| | 2 | A | + | | 3 | B | + | | 4 | C | + | | D | + | | 2 | E | = | | 0 | | (2) |
| | A | + | | 2 | B | + | | C | + | | 3 | D | + | | E | = | | 0 | | (3) |
| | 4 | A | + | | 2 | B | + | | 4 | C | + | | 5 | D | + | | 3 | E | = | | 0 | | (4) |
| | 2 | A | + | | 2 | B | + | | 3 | C | + | | 4 | D | + | | 5 | E | = | | 0 | | (5) |
| Question solving process:
Multiply both sides of equation (1) by 2, the equation can be obtained: | | 2 | A | + | | 2 | B | + | | 4 | C | + | | 6 | D | + | | 10 | E | = | | 0 | (6) | , then subtract both sides of equation (6) from both sides of equation (2), the equations are reduced to:
| | | | A | + | | B | + | | 2 | C | + | | 3 | D | + | | 5 | E | = | | 0 | | (1) |
| | | A | + | | 2 | B | + | | C | + | | 3 | D | + | | E | = | | 0 | | (3) |
| | 4 | A | + | | 2 | B | + | | 4 | C | + | | 5 | D | + | | 3 | E | = | | 0 | | (4) |
| | 2 | A | + | | 2 | B | + | | 3 | C | + | | 4 | D | + | | 5 | E | = | | 0 | | (5) |
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Subtract both sides of equation (1) from both sides of equation (3) ,the equations are reduced to:
| | | | A | + | | B | + | | 2 | C | + | | 3 | D | + | | 5 | E | = | | 0 | | (1) |
| | | | 4 | A | + | | 2 | B | + | | 4 | C | + | | 5 | D | + | | 3 | E | = | | 0 | | (4) |
| | 2 | A | + | | 2 | B | + | | 3 | C | + | | 4 | D | + | | 5 | E | = | | 0 | | (5) |
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Multiply both sides of equation (1) by 4, the equation can be obtained: | | 4 | A | + | | 4 | B | + | | 8 | C | + | | 12 | D | + | | 20 | E | = | | 0 | (7) | , then subtract both sides of equation (7) from both sides of equation (4), the equations are reduced to:
| | | | A | + | | B | + | | 2 | C | + | | 3 | D | + | | 5 | E | = | | 0 | | (1) |
| | | | | 2 | A | + | | 2 | B | + | | 3 | C | + | | 4 | D | + | | 5 | E | = | | 0 | | (5) |
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Multiply both sides of equation (1) by 2, the equation can be obtained: | | 2 | A | + | | 2 | B | + | | 4 | C | + | | 6 | D | + | | 10 | E | = | | 0 | (8) | , then subtract both sides of equation (8) from both sides of equation (5), the equations are reduced to:
| | | | A | + | | B | + | | 2 | C | + | | 3 | D | + | | 5 | E | = | | 0 | | (1) |
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Subtract both sides of equation (2) from both sides of equation (3) ,the equations are reduced to:
| | | | A | + | | B | + | | 2 | C | + | | 3 | D | + | | 5 | E | = | | 0 | | (1) |
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Multiply both sides of equation (2) by 2, the equation can be obtained: , then add the two sides of equation (9) to both sides of equation (4), the equations are reduced to:
| | | | A | + | | B | + | | 2 | C | + | | 3 | D | + | | 5 | E | = | | 0 | | (1) |
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Multiply both sides of equation (3) by 4, the equation can be obtained: , then subtract both sides of equation (10) from both sides of equation (4), the equations are reduced to:
| | | | A | + | | B | + | | 2 | C | + | | 3 | D | + | | 5 | E | = | | 0 | | (1) |
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Subtract both sides of equation (3) from both sides of equation (5) ,the equations are reduced to:
| | | | A | + | | B | + | | 2 | C | + | | 3 | D | + | | 5 | E | = | | 0 | | (1) |
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Multiply both sides of equation (4) by 7 Divide the two sides of equation (4) by 37, the equation can be obtained: , then subtract both sides of equation (11) from both sides of equation (5), the equations are reduced to:
| | | | A | + | | B | + | | 2 | C | + | | 3 | D | + | | 5 | E | = | | 0 | | (1) |
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Multiply both sides of equation (5) by 1813 Divide both sides of equation (5) by 10, get the equation:, then add the two sides of equation (12) to both sides of equation (4), get the equation:
| | | | A | + | | B | + | | 2 | C | + | | 3 | D | + | | 5 | E | = | | 0 | | (1) |
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Multiply both sides of equation (5) by 74 Divide both sides of equation (5) by 5, get the equation:, then subtract both sides of equation (13) from both sides of equation (3), get the equation:
| | | | A | + | | B | + | | 2 | C | + | | 3 | D | + | | 5 | E | = | | 0 | | (1) |
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Multiply both sides of equation (5) by 148 Divide both sides of equation (5) by 5, get the equation:, then add the two sides of equation (14) to both sides of equation (2), get the equation:
| | | | A | + | | B | + | | 2 | C | + | | 3 | D | + | | 5 | E | = | | 0 | | (1) |
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Multiply both sides of equation (5) by 37 Divide both sides of equation (5) by 2, get the equation:, then subtract both sides of equation (15) from both sides of equation (1), get the equation:
Multiply both sides of equation (4) by 5 Divide both sides of equation (4) by 37, get the equation:, then add the two sides of equation (16) to both sides of equation (3), get the equation:
Multiply both sides of equation (4) by 5 Divide both sides of equation (4) by 37, get the equation:, then subtract both sides of equation (17) from both sides of equation (2), get the equation:
Multiply both sides of equation (4) by 3 Divide both sides of equation (4) by 37, get the equation:, then add the two sides of equation (18) to both sides of equation (1), get the equation:
Multiply both sides of equation (3) by 2, get the equation:, then add the two sides of equation (19) to both sides of equation (1), get the equation:
Subtract both sides of equation (2) 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:
解方程组的详细方法请参阅:《多元一次方程组的解法》 |