detailed information: The input equation set is:
| | | | | 43 2 | x | | - | 35 2 | y | | - | 5 2 | z | = | | 0 | | (1) |
| - | 35 2 | x | + | | | 51 2 | y | + | | | 21 2 | z | = | | -14 | | (2) |
| - | 5 2 | x | + | | | 21 2 | y | + | | | 25 2 | z | = | | -14 | | (3) |
| Question solving process:
Multiply both sides of equation (1) by 35 Divide the two sides of equation (1) by 43, the equation can be obtained: | | | 35 2 | x | | - | 1225 86 | y | | - | 175 86 | z | = | | 0 | (4) | , then add the two sides of equation (4) to both sides of equation (2), the equations are reduced to:
| | | | | 43 2 | x | | - | 35 2 | y | | - | 5 2 | z | = | | 0 | | (1) |
| | | 484 43 | y | + | | | 364 43 | z | = | | -14 | | (2) |
| - | 5 2 | x | + | | | 21 2 | y | + | | | 25 2 | z | = | | -14 | | (3) |
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Multiply both sides of equation (1) by 5 Divide the two sides of equation (1) by 43, the equation can be obtained: | | | 5 2 | x | | - | 175 86 | y | | - | 25 86 | z | = | | 0 | (5) | , then add the two sides of equation (5) to both sides of equation (3), the equations are reduced to:
| | | | | 43 2 | x | | - | 35 2 | y | | - | 5 2 | z | = | | 0 | | (1) |
| | | 484 43 | y | + | | | 364 43 | z | = | | -14 | | (2) |
| | | 364 43 | y | + | | | 525 43 | z | = | | -14 | | (3) |
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Multiply both sides of equation (2) by 91 Divide the two sides of equation (2) by 121, the equation can be obtained: | | | 364 43 | y | + | | | 33124 5203 | z | = | | - | 1274 121 | (6) | , then subtract both sides of equation (6) from both sides of equation (3), the equations are reduced to:
| | | | | 43 2 | x | | - | 35 2 | y | | - | 5 2 | z | = | | 0 | | (1) |
| | | 484 43 | y | + | | | 364 43 | z | = | | -14 | | (2) |
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Multiply both sides of equation (3) by 6292 Divide both sides of equation (3) by 4343, get the equation: | | | 36764 4343 | z | = | | - | 21840 4343 | (7) | , then subtract both sides of equation (7) from both sides of equation (2), get the equation:
| | | | | 43 2 | x | | - | 35 2 | y | | - | 5 2 | z | = | | 0 | | (1) |
| | |
Multiply both sides of equation (3) by 605 Divide both sides of equation (3) by 1414, get the equation:, then add the two sides of equation (8) to both sides of equation (1), get the equation:
| | | | | 43 2 | x | | - | 35 2 | y | = | | - | 150 101 | | (1) |
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Multiply both sides of equation (2) by 1505 Divide both sides of equation (2) by 968, 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:
Convert the solution of the equation set to decimals:
解方程组的详细方法请参阅:《多元一次方程组的解法》 |