detailed information: The input equation set is:
| | | | | 16 | A | + | | 8 | B | + | | 4 | C | + | | 2 | D | = | | 0 | | (2) |
| | 256 | A | + | | 64 | B | + | | 16 | C | + | | 4 | D | = | | 0 | | (3) |
| | 4096 | A | + | | 512 | B | + | | 64 | C | + | | 8 | D | = | | 0 | | (4) |
| Question solving process:
Multiply both sides of equation (1) by 16, the equation can be obtained: | | 16 | A | + | | 16 | B | + | | 16 | C | + | | 16 | D | = | | 0 | (5) | , then subtract both sides of equation (5) from both sides of equation (2), the equations are reduced to:
| | | | | | 256 | A | + | | 64 | B | + | | 16 | C | + | | 4 | D | = | | 0 | | (3) |
| | 4096 | A | + | | 512 | B | + | | 64 | C | + | | 8 | D | = | | 0 | | (4) |
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Multiply both sides of equation (1) by 256, the equation can be obtained: | | 256 | A | + | | 256 | B | + | | 256 | C | + | | 256 | D | = | | 0 | (6) | , then subtract both sides of equation (6) from both sides of equation (3), the equations are reduced to:
| | | | | -192 | B | | -240 | C | | -252 | D | = | | 0 | | (3) |
| | 4096 | A | + | | 512 | B | + | | 64 | C | + | | 8 | D | = | | 0 | | (4) |
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Multiply both sides of equation (1) by 4096, the equation can be obtained: | | 4096 | A | + | | 4096 | B | + | | 4096 | C | + | | 4096 | D | = | | 0 | (7) | , then subtract both sides of equation (7) from both sides of equation (4), the equations are reduced to:
| | | | | -192 | B | | -240 | C | | -252 | D | = | | 0 | | (3) |
| -3584 | B | | -4032 | C | | -4088 | D | = | | 0 | | (4) |
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Multiply both sides of equation (2) by 24, the equation can be obtained: | -192 | B | | -288 | C | | -336 | D | = | | 0 | (8) | , then subtract both sides of equation (8) from both sides of equation (3), the equations are reduced to:
| | | | | | -3584 | B | | -4032 | C | | -4088 | D | = | | 0 | | (4) |
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Multiply both sides of equation (2) by 448, the equation can be obtained: | -3584 | B | | -5376 | C | | -6272 | D | = | | 0 | (9) | , 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 28, the equation can be obtained: , then subtract both sides of equation (10) from both sides of equation (4), the equations are reduced to:
Divide both sides of equation (4) by 2, get the equation:, then add the two sides of equation (11) to both sides of equation (3), get the equation:
Divide both sides of equation (4) by 12, 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 168, get the equation:, then add the two sides of equation (13) to both sides of equation (1), get the equation:
Divide both sides of equation (3) by 4, get the equation:, then add the two sides of equation (14) to both sides of equation (2), get the equation:
Divide both sides of equation (3) by 48, get the equation:, then subtract both sides of equation (15) from both sides of equation (1), get the equation:
Divide both sides of equation (2) by 8, 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:
解方程组的详细方法请参阅:《多元一次方程组的解法》 |