detailed information: The input equation set is:
| | | | 2 | A | + | | 2 | B | + | | 4 | C | + | | D | + | | 3 | E | = | | | 981 5 | | (1) |
| | | | 2 | A | + | | B | + | | 2 | C | + | | D | + | | E | = | | 100 | | (4) |
| | Question solving process:
Divide the two sides of equation (1) by 2, the equation can be obtained: | | A | + | | B | + | | 2 | C | + | | | 1 2 | D | + | | | 3 2 | E | = | | | 981 10 | (6) | , then subtract both sides of equation (6) from both sides of equation (3), the equations are reduced to:
| | | | 2 | A | + | | 2 | B | + | | 4 | C | + | | D | + | | 3 | E | = | | | 981 5 | | (1) |
| | -1 | C | | - | 1 2 | D | | - | 1 2 | E | = | | - | 98 5 | | (3) |
| | 2 | A | + | | B | + | | 2 | C | + | | D | + | | E | = | | 100 | | (4) |
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Subtract both sides of equation (1) from both sides of equation (4) ,the equations are reduced to:
| | | | 2 | A | + | | 2 | B | + | | 4 | C | + | | D | + | | 3 | E | = | | | 981 5 | | (1) |
| | -1 | C | | - | 1 2 | D | | - | 1 2 | E | = | | - | 98 5 | | (3) |
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Subtract both sides of equation (1) from both sides of equation (5) ,the equations are reduced to:
| | | | 2 | A | + | | 2 | B | + | | 4 | C | + | | D | + | | 3 | E | = | | | 981 5 | | (1) |
| | -1 | C | | - | 1 2 | D | | - | 1 2 | E | = | | - | 98 5 | | (3) |
| | -1 | B | | -4 | C | | -1 | D | | -3 | E | = | | - | 677 5 | | (5) |
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交After the exchange of equation (2) and equation (4), the equation system becomes:
| | | | 2 | A | + | | 2 | B | + | | 4 | C | + | | D | + | | 3 | E | = | | | 981 5 | | (1) |
| | -1 | C | | - | 1 2 | D | | - | 1 2 | E | = | | - | 98 5 | | (3) |
| | -1 | B | | -4 | C | | -1 | D | | -3 | E | = | | - | 677 5 | | (5) |
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Subtract both sides of equation (2) from both sides of equation (5) ,the equations are reduced to:
| | | | 2 | A | + | | 2 | B | + | | 4 | C | + | | D | + | | 3 | E | = | | | 981 5 | | (1) |
| | -1 | C | | - | 1 2 | D | | - | 1 2 | E | = | | - | 98 5 | | (3) |
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Multiply both sides of equation (3) by 2, the equation can be obtained: , then add the two sides of equation (7) to both sides of equation (4), the equations are reduced to:
| | | | 2 | A | + | | 2 | B | + | | 4 | C | + | | D | + | | 3 | E | = | | | 981 5 | | (1) |
| | -1 | C | | - | 1 2 | D | | - | 1 2 | E | = | | - | 98 5 | | (3) |
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Multiply both sides of equation (3) by 2, the equation can be obtained: , then subtract both sides of equation (8) from both sides of equation (5), the equations are reduced to:
| | | | 2 | A | + | | 2 | B | + | | 4 | C | + | | D | + | | 3 | E | = | | | 981 5 | | (1) |
| | -1 | C | | - | 1 2 | D | | - | 1 2 | E | = | | - | 98 5 | | (3) |
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Multiply both sides of equation (3) by 2, get the equation:, then subtract both sides of equation (9) from both sides of equation (2), get the equation:
| | | | 2 | A | + | | 2 | B | + | | 4 | C | + | | D | + | | 3 | E | = | | | 981 5 | | (1) |
| | -1 | C | | - | 1 2 | D | | - | 1 2 | E | = | | - | 98 5 | | (3) |
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Multiply both sides of equation (3) by 4, get the equation: | -4 | C | | -2 | D | | -2 | E | = | | - | 392 5 | (10) | , then add the two sides of equation (10) to both sides of equation (1), get the equation:
| | | | 2 | A | + | | 2 | B | | -1 | D | + | | E | = | | | 589 5 | | (1) |
| | -1 | C | | - | 1 2 | D | | - | 1 2 | E | = | | - | 98 5 | | (3) |
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Multiply both sides of equation (2) by 2, get the equation:, then add the two sides of equation (11) 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:
| | | | | C = | | 19.600000 | - | | | 1 2 | D | - | | | 1 2 | E |
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Where: D, 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》 |