detailed information: The input equation set is:
 | | | | - | 9 10 | x | + | | | 1 10 | y | + | | | 1 5 | z | = | | 0 | | (1) |
| | | Question solving process:
Divide the two sides of equation (1) by 9, the equation can be obtained: | | - | 1 10 | x | + | | | 1 90 | y | + | | | 1 45 | z | = | | 0 | (4) | , then add the two sides of equation (4) to both sides of equation (3), the equations are reduced to:
 | | | | - | 9 10 | x | + | | | 1 10 | y | + | | | 1 5 | z | = | | 0 | | (1) |
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Divide the two sides of equation (2) by 81, the equation can be obtained: , then add the two sides of equation (5) to both sides of equation (3), the equations are reduced to:
 | | | | - | 9 10 | x | + | | | 1 10 | y | + | | | 1 5 | z | = | | 0 | | (1) |
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Multiply both sides of equation (3) by 81 Divide both sides of equation (3) by 829, get the equation:, then subtract both sides of equation (6) from both sides of equation (2), get the equation:
 | | | | - | 9 10 | x | + | | | 1 10 | y | + | | | 1 5 | z | = | | 0 | | (1) |
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Multiply both sides of equation (3) by 162 Divide both sides of equation (3) by 829, get the equation:, then subtract both sides of equation (7) from both sides of equation (1), get the equation:
Divide both sides of equation (2) by 9, get the equation:, then add the two sides of equation (8) 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》 |