detailed information: The input equation set is:
| | | | | | 10 | A | | -13 | B | | -1 | C | + | | 2 | D | = | | 10 | | (3) |
| | Question solving process:
Multiply both sides of equation (1) by 4, the equation can be obtained: | | 4 | A | + | | 8 | B | | -16 | C | + | | 20 | D | = | | -8 | (5) | , then subtract both sides of equation (5) from both sides of equation (2), the equations are reduced to:
| | | | | | 10 | A | | -13 | B | | -1 | C | + | | 2 | D | = | | 10 | | (3) |
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Multiply both sides of equation (1) by 10, the equation can be obtained: | | 10 | A | + | | 20 | B | | -40 | C | + | | 50 | D | = | | -20 | (6) | , then subtract both sides of equation (6) from both sides of equation (3), the equations are reduced to:
Multiply both sides of equation (2) by 3, the equation can be obtained: , then subtract both sides of equation (7) from both sides of equation (3), the equations are reduced to:
Multiply both sides of equation (2) by 2 Divide both sides of equation (2) by 11, get the equation: | -2 | B | + | | | 26 11 | C | | - | 32 11 | D | = | | | 20 11 | (8) | , then add the two sides of equation (8) to both sides of equation (1), get the equation:
| | | | A | | - | 18 11 | C | + | | | 23 11 | D | = | | - | 2 11 | | (1) |
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The coefficient of the unknown number is reduced to 1, and the equations are reduced to:
| | | | A | | - | 18 11 | C | + | | | 23 11 | D | = | | - | 2 11 | | (1) |
| | B | | - | 13 11 | C | + | | | 16 11 | D | = | | - | 10 11 | | (2) |
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Therefore, the solution of the equation set is:
| | | A = | | - | 2 11 | + | | | 18 11 | C | - | | | 23 11 | D |
| B = | | - | 10 11 | + | | | 13 11 | C | - | | | 16 11 | D |
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Convert the solution of the equation set to decimals:
| | | A = | | -0.181818 | + | | | 18 11 | C | - | | | 23 11 | D |
| B = | | -0.909091 | + | | | 13 11 | C | - | | | 16 11 | D |
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Where: C, D are arbitrary constants. 解方程组的详细方法请参阅:《多元一次方程组的解法》 |