detailed information: The input equation set is:
| | | - | 1 5 | x | + | | | 1 2 | y | + | | | 1 2 | z | = | | 0 | | (1) |
| | | 1 10 | x | | - | 9 10 | y | + | | | 9 10 | z | = | | 0 | | (2) |
| | | 9 10 | x | | - | 9 10 | y | + | | | 9 10 | z | = | | 0 | | (3) |
| Question solving process:
Divide the two sides of equation (1) by 2, the equation can be obtained: | - | 1 10 | x | + | | | 1 4 | y | + | | | 1 4 | z | = | | 0 | (4) | , then add the two sides of equation (4) to both sides of equation (2), the equations are reduced to:
| | | - | 1 5 | x | + | | | 1 2 | y | + | | | 1 2 | z | = | | 0 | | (1) |
| | | | 9 10 | x | | - | 9 10 | y | + | | | 9 10 | z | = | | 0 | | (3) |
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Multiply both sides of equation (1) by 9 Divide the two sides of equation (1) by 2, the equation can be obtained: | - | 9 10 | x | + | | | 9 4 | y | + | | | 9 4 | z | = | | 0 | (5) | , then add the two sides of equation (5) to both sides of equation (3), the equations are reduced to:
| | | - | 1 5 | x | + | | | 1 2 | y | + | | | 1 2 | z | = | | 0 | | (1) |
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Multiply both sides of equation (2) by 27 Divide the two sides of equation (2) by 13, the equation can be obtained: | - | 27 20 | y | + | | | 621 260 | z | = | | 0 | (6) | , then add the two sides of equation (6) to both sides of equation (3), the equations are reduced to:
| | | - | 1 5 | x | + | | | 1 2 | y | + | | | 1 2 | z | = | | 0 | | (1) |
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Multiply both sides of equation (3) by 299 Divide both sides of equation (3) by 1440, get the equation:, then subtract both sides of equation (7) from both sides of equation (2), get the equation:
| | | - | 1 5 | x | + | | | 1 2 | y | + | | | 1 2 | z | = | | 0 | | (1) |
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Multiply both sides of equation (3) by 13 Divide both sides of equation (3) by 144, get the equation:, then subtract both sides of equation (8) from both sides of equation (1), get the equation:
Multiply both sides of equation (2) by 10 Divide both sides of equation (2) by 13, get the equation:, then add the two sides of equation (9) 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》 |