detailed information: The input equation set is:
| | | | | 9 | A | + | | 8 | B | + | | 7 | C | + | | 6 | D | = | | 0 | | (2) |
| | 26 | A | + | | 19 | B | + | | 14 | C | + | | 9 | D | = | | 0 | | (3) |
| | 24 | A | + | | 12 | B | + | | 8 | C | + | | 6 | D | = | | 0 | | (4) |
| Question solving process:
Multiply both sides of equation (1) by 9, the equation can be obtained: | | 9 | A | + | | 9 | B | + | | 9 | C | + | | 9 | D | = | | 0 | (5) | , then subtract both sides of equation (5) from both sides of equation (2), the equations are reduced to:
| | | | | | 26 | A | + | | 19 | B | + | | 14 | C | + | | 9 | D | = | | 0 | | (3) |
| | 24 | A | + | | 12 | B | + | | 8 | C | + | | 6 | D | = | | 0 | | (4) |
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Multiply both sides of equation (1) by 26, the equation can be obtained: | | 26 | A | + | | 26 | B | + | | 26 | C | + | | 26 | D | = | | 0 | (6) | , then subtract both sides of equation (6) from both sides of equation (3), the equations are reduced to:
| | | | | | | 24 | A | + | | 12 | B | + | | 8 | C | + | | 6 | D | = | | 0 | | (4) |
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Multiply both sides of equation (1) by 24, the equation can be obtained: | | 24 | A | + | | 24 | B | + | | 24 | C | + | | 24 | D | = | | 0 | (7) | , then subtract both sides of equation (7) from both sides of equation (4), the equations are reduced to:
Multiply both sides of equation (2) by 7, the equation can be obtained: , then subtract both sides of equation (8) from both sides of equation (3), the equations are reduced to:
Multiply both sides of equation (2) by 12, the equation can be obtained: , then subtract both sides of equation (9) from both sides of equation (4), the equations are reduced to:
Multiply both sides of equation (3) by 4, the equation can be obtained: , then subtract both sides of equation (10) from both sides of equation (4), the equations are reduced to:
Multiply both sides of equation (4) by 2, get the equation:, then subtract both sides of equation (11) from both sides of equation (3), get the equation:
Multiply both sides of equation (4) by 3 Divide both sides of equation (4) by 2, get the equation:, then add the two sides of equation (12) to both sides of equation (2), get the equation:
Divide both sides of equation (4) by 2, get the equation:, then subtract both sides of equation (13) from both sides of equation (1), get the equation:
Add both sides of equation (3) to both sides of equation (2), get the equation:
Divide both sides of equation (3) by 2, get the equation:, then subtract both sides of equation (14) from both sides of equation (1), get the equation:
Add both sides of equation (2) 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》 |