detailed information: The input equation set is: Question solving process:
Divide the two sides of equation (1) by 5, the equation can be obtained: | | A | | - | 1 5 | B | | - | 1 5 | C | | - | 3 5 | D | = | | 0 | (5) | , then add the two sides of equation (5) to both sides of equation (2), the equations are reduced to:
| | | | | | 24 5 | B | | - | 6 5 | C | | - | 18 5 | D | = | | 0 | | (2) |
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Divide the two sides of equation (1) by 5, the equation can be obtained: | | A | | - | 1 5 | B | | - | 1 5 | C | | - | 3 5 | D | = | | 0 | (6) | , then subtract both sides of equation (6) from both sides of equation (3), the equations are reduced to:
| | | | | | 24 5 | B | | - | 6 5 | C | | - | 18 5 | D | = | | 0 | | (2) |
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Divide the two sides of equation (1) by 5, the equation can be obtained: | | A | | - | 1 5 | B | | - | 1 5 | C | | - | 3 5 | D | = | | 0 | (7) | , then add the two sides of equation (7) to both sides of equation (4), the equations are reduced to:
| | | | | | 24 5 | B | | - | 6 5 | C | | - | 18 5 | D | = | | 0 | | (2) |
| | - | 6 5 | B | + | | | 24 5 | C | | - | 18 5 | D | = | | 0 | | (4) |
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Divide the two sides of equation (2) by 4, the equation can be obtained: | | | 6 5 | B | | - | 3 10 | C | | - | 9 10 | D | = | | 0 | (8) | , then subtract both sides of equation (8) from both sides of equation (3), the equations are reduced to:
| | | | | | 24 5 | B | | - | 6 5 | C | | - | 18 5 | D | = | | 0 | | (2) |
| | - | 6 5 | B | + | | | 24 5 | C | | - | 18 5 | D | = | | 0 | | (4) |
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Divide the two sides of equation (2) by 4, the equation can be obtained: | | | 6 5 | B | | - | 3 10 | C | | - | 9 10 | D | = | | 0 | (9) | , then add the two sides of equation (9) to both sides of equation (4), the equations are reduced to:
| | | | | | 24 5 | B | | - | 6 5 | C | | - | 18 5 | D | = | | 0 | | (2) |
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Multiply both 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:
| | | | | | 24 5 | B | | - | 6 5 | C | | - | 18 5 | D | = | | 0 | | (2) |
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Multiply both sides of equation (4) by 5 Divide both sides of equation (4) by 24, get the equation:, then add the two sides of equation (11) to both sides of equation (3), get the equation:
| | | | | | 24 5 | B | | - | 6 5 | C | | - | 18 5 | D | = | | 0 | | (2) |
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Multiply both sides of equation (4) by 3 Divide both sides of equation (4) by 10, get the equation:, then subtract both sides of equation (12) from both sides of equation (2), get the equation:
Divide both sides of equation (4) by 4, get the equation:, then subtract both sides of equation (13) from both sides of equation (1), get the equation:
Multiply both sides of equation (3) by 4 Divide both sides of equation (3) by 5, get the equation:, then add the two sides of equation (14) to both sides of equation (2), get the equation:
Multiply both sides of equation (3) by 2 Divide both sides of equation (3) by 3, get the equation:, then add the two sides of equation (15) to both sides of equation (1), get the equation:
Multiply both sides of equation (2) by 5 Divide both sides of equation (2) by 24, get the equation:, then add the two sides of equation (16) 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》 |