detailed information: The input equation set is:
| | | | | 69 500 | x | + | | | 89 500 | y | + | | | 17 100 | z | = | | 0 | | (1) |
| | | 17 100 | x | + | | | 17 100 | y | + | | | 17 100 | z | = | | 0 | | (2) |
| | | 17 100 | x | + | | | 17 100 | y | + | | | 17 100 | z | = | | 0 | | (3) |
| Question solving process:
Multiply both sides of equation (1) by 85 Divide the two sides of equation (1) by 69, the equation can be obtained: | | | 17 100 | x | + | | | 1513 6900 | y | + | | | 289 1380 | z | = | | 0 | (4) | , then subtract both sides of equation (4) from both sides of equation (2), the equations are reduced to:
| | | | | 69 500 | x | + | | | 89 500 | y | + | | | 17 100 | z | = | | 0 | | (1) |
| - | 17 345 | y | | - | 68 1725 | z | = | | 0 | | (2) |
| | | 17 100 | x | + | | | 17 100 | y | + | | | 17 100 | z | = | | 0 | | (3) |
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Multiply both sides of equation (1) by 85 Divide the two sides of equation (1) by 69, the equation can be obtained: | | | 17 100 | x | + | | | 1513 6900 | y | + | | | 289 1380 | z | = | | 0 | (5) | , then subtract both sides of equation (5) from both sides of equation (3), the equations are reduced to:
| | | | | 69 500 | x | + | | | 89 500 | y | + | | | 17 100 | z | = | | 0 | | (1) |
| - | 17 345 | y | | - | 68 1725 | z | = | | 0 | | (2) |
| - | 17 345 | y | | - | 68 1725 | z | = | | 0 | | (3) |
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Subtract both sides of equation (2) from both sides of equation (3) ,the equations are reduced to:
| | | | | 69 500 | x | + | | | 89 500 | y | + | | | 17 100 | z | = | | 0 | | (1) |
| - | 17 345 | y | | - | 68 1725 | z | = | | 0 | | (2) |
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Multiply both sides of equation (2) by 6141 Divide both sides of equation (2) by 1700, get the equation: | - | 89 500 | y | | - | 89 625 | z | = | | 0 | (6) | , then add the two sides of equation (6) to both sides of equation (1), get the equation:
| | | | - | 17 345 | y | | - | 68 1725 | z | = | | 0 | | (2) |
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The coefficient of the unknown number is reduced to 1, and the equations are reduced to:
Therefore, the solution of the equation set is:
Where: z 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》 |