detailed information: The input equation set is:
| | | | | -2 | A | | -1 | B | + | | 4 | C | | -2 | D | = | | -3 | | (3) |
| | Question solving process:
Divide the two sides of equation (1) by 3, the equation can be obtained: | | A | + | | | 1 3 | B | | - | 2 3 | C | + | | | 1 3 | D | = | | - | 7 3 | (5) | , then subtract both sides of equation (5) from both sides of equation (2), the equations are reduced to:
| | | | | | 8 3 | B | | - | 1 3 | C | | - | 1 3 | D | = | | - | 14 3 | | (2) |
| -2 | A | | -1 | B | + | | 4 | C | | -2 | D | = | | -3 | | (3) |
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Multiply both sides of equation (1) by 2 Divide the two sides of equation (1) by 3, the equation can be obtained: | | 2 | A | + | | | 2 3 | B | | - | 4 3 | C | + | | | 2 3 | D | = | | - | 14 3 | (6) | , then add the two sides of equation (6) to both sides of equation (3), the equations are reduced to:
| | | | | | 8 3 | B | | - | 1 3 | C | | - | 1 3 | D | = | | - | 14 3 | | (2) |
| - | 1 3 | B | + | | | 8 3 | C | | - | 4 3 | D | = | | - | 23 3 | | (3) |
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Divide the two sides of equation (1) by 3, the equation can be obtained: | | A | + | | | 1 3 | B | | - | 2 3 | C | + | | | 1 3 | D | = | | - | 7 3 | (7) | , then subtract both sides of equation (7) from both sides of equation (4), the equations are reduced to:
| | | | | | 8 3 | B | | - | 1 3 | C | | - | 1 3 | D | = | | - | 14 3 | | (2) |
| - | 1 3 | B | + | | | 8 3 | C | | - | 4 3 | D | = | | - | 23 3 | | (3) |
| - | 1 3 | B | | - | 4 3 | C | + | | | 8 3 | D | = | | | 19 3 | | (4) |
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Divide the two sides of equation (2) by 8, the equation can be obtained: | | | 1 3 | B | | - | 1 24 | C | | - | 1 24 | D | = | | - | 7 12 | (8) | , then add the two sides of equation (8) to both sides of equation (3), the equations are reduced to:
| | | | | | 8 3 | B | | - | 1 3 | C | | - | 1 3 | D | = | | - | 14 3 | | (2) |
| | - | 1 3 | B | | - | 4 3 | C | + | | | 8 3 | D | = | | | 19 3 | | (4) |
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Divide the two sides of equation (2) by 8, the equation can be obtained: | | | 1 3 | B | | - | 1 24 | C | | - | 1 24 | D | = | | - | 7 12 | (9) | , then add the two sides of equation (9) to both sides of equation (4), the equations are reduced to:
| | | | | | 8 3 | B | | - | 1 3 | C | | - | 1 3 | D | = | | - | 14 3 | | (2) |
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Multiply both sides of equation (3) by 11 Divide the two sides of equation (3) by 21, the equation can be obtained: | | | 11 8 | C | | - | 121 168 | D | = | | - | 121 28 | (10) | , then add the two sides of equation (10) to both sides of equation (4), the equations are reduced to:
| | | | | | 8 3 | B | | - | 1 3 | C | | - | 1 3 | D | = | | - | 14 3 | | (2) |
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Multiply both sides of equation (4) by 231 Divide both sides of equation (4) by 320, get the equation:, then add the two sides of equation (11) to both sides of equation (3), get the equation:
| | | | | | 8 3 | B | | - | 1 3 | C | | - | 1 3 | D | = | | - | 14 3 | | (2) |
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Multiply both sides of equation (4) by 7 Divide both sides of equation (4) by 40, get the equation:, then add the two sides of equation (12) to both sides of equation (2), get the equation:
Multiply both sides of equation (4) by 21 Divide both sides of equation (4) by 40, 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 8 Divide both sides of equation (3) by 63, 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 16 Divide both sides of equation (3) by 21, 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 3 Divide both sides of equation (2) by 8, get the equation:, then subtract both sides of equation (16) from 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》 |