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