detailed information: The input equation set is:
| | | - | 1 2 | A | + | | | 1 2 | B | + | | | 1 4 | C | = | | 0 | | (1) |
| | | | Question solving process:
Divide the two sides of equation (1) by 2, the equation can be obtained: | - | 1 4 | A | + | | | 1 4 | B | + | | | 1 8 | C | = | | 0 | (5) | , then add the two sides of equation (5) to both sides of equation (2), the equations are reduced to:
| | | - | 1 2 | A | + | | | 1 2 | B | + | | | 1 4 | C | = | | 0 | | (1) |
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Divide the two sides of equation (1) by 2, the equation can be obtained: | - | 1 4 | A | + | | | 1 4 | B | + | | | 1 8 | C | = | | 0 | (6) | , then add the two sides of equation (6) to both sides of equation (3), the equations are reduced to:
| | | - | 1 2 | A | + | | | 1 2 | B | + | | | 1 4 | C | = | | 0 | | (1) |
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Multiply both sides of equation (1) 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:
| | | - | 1 2 | A | + | | | 1 2 | B | + | | | 1 4 | C | = | | 0 | | (1) |
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Multiply both sides of equation (2) by 3 Divide the two sides of equation (2) by 5, the equation can be obtained: , then add the two sides of equation (8) to both sides of equation (3), the equations are reduced to:
| | | - | 1 2 | A | + | | | 1 2 | B | + | | | 1 4 | C | = | | 0 | | (1) |
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Multiply both sides of equation (2) by 8 Divide the two sides of equation (2) by 3, the equation can be obtained: , then add the two sides of equation (9) to both sides of equation (4), the equations are reduced to:
| | | - | 1 2 | A | + | | | 1 2 | B | + | | | 1 4 | C | = | | 0 | | (1) |
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Multiply both sides of equation (3) by 50 Divide the two sides of equation (3) by 3, the equation can be obtained: , then subtract both sides of equation (10) from both sides of equation (4), the equations are reduced to:
| | | - | 1 2 | A | + | | | 1 2 | B | + | | | 1 4 | C | = | | 0 | | (1) |
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由第(4)方程式可以看出,该方程组无解。
解方程组的详细方法请参阅:《多元一次方程组的解法》 |