detailed information: The input equation set is:
| | | | | A | + | | B | + | | C | + | | D | + | | E | = | | 1 | | (2) |
| | 16 | A | + | | 8 | B | + | | 4 | C | + | | 2 | D | + | | E | = | | 5 | | (3) |
| | 81 | A | + | | 27 | B | + | | 9 | C | + | | 3 | D | + | | E | = | | 13 | | (4) |
| | 256 | A | + | | 64 | B | + | | 16 | C | + | | 4 | D | + | | E | = | | 27 | | (5) |
| Question solving process:
交After the exchange of equation (1) and equation (2), the equation system becomes:
| | | | A | + | | B | + | | C | + | | D | + | | E | = | | 1 | | (1) |
| | | 16 | A | + | | 8 | B | + | | 4 | C | + | | 2 | D | + | | E | = | | 5 | | (3) |
| | 81 | A | + | | 27 | B | + | | 9 | C | + | | 3 | D | + | | E | = | | 13 | | (4) |
| | 256 | A | + | | 64 | B | + | | 16 | C | + | | 4 | D | + | | E | = | | 27 | | (5) |
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Multiply both sides of equation (1) by 16, the equation can be obtained: | | 16 | A | + | | 16 | B | + | | 16 | C | + | | 16 | D | + | | 16 | E | = | | 16 | (6) | , then subtract both sides of equation (6) from both sides of equation (3), the equations are reduced to:
| | | | A | + | | B | + | | C | + | | D | + | | E | = | | 1 | | (1) |
| | -8 | B | | -12 | C | | -14 | D | | -15 | E | = | | -11 | | (3) |
| | 81 | A | + | | 27 | B | + | | 9 | C | + | | 3 | D | + | | E | = | | 13 | | (4) |
| | 256 | A | + | | 64 | B | + | | 16 | C | + | | 4 | D | + | | E | = | | 27 | | (5) |
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Multiply both sides of equation (1) by 81, the equation can be obtained: | | 81 | A | + | | 81 | B | + | | 81 | C | + | | 81 | D | + | | 81 | E | = | | 81 | (7) | , then subtract both sides of equation (7) from both sides of equation (4), the equations are reduced to:
| | | | A | + | | B | + | | C | + | | D | + | | E | = | | 1 | | (1) |
| | -8 | B | | -12 | C | | -14 | D | | -15 | E | = | | -11 | | (3) |
| -54 | B | | -72 | C | | -78 | D | | -80 | E | = | | -68 | | (4) |
| | 256 | A | + | | 64 | B | + | | 16 | C | + | | 4 | D | + | | E | = | | 27 | | (5) |
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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 | + | | 256 | E | = | | 256 | (8) | , then subtract both sides of equation (8) from both sides of equation (5), the equations are reduced to:
| | | | A | + | | B | + | | C | + | | D | + | | E | = | | 1 | | (1) |
| | -8 | B | | -12 | C | | -14 | D | | -15 | E | = | | -11 | | (3) |
| -54 | B | | -72 | C | | -78 | D | | -80 | E | = | | -68 | | (4) |
| -192 | B | | -240 | C | | -252 | D | | -255 | E | = | | -229 | | (5) |
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交After the exchange of equation (2) and equation (3), the equation system becomes:
| | | | A | + | | B | + | | C | + | | D | + | | E | = | | 1 | | (1) |
| -8 | B | | -12 | C | | -14 | D | | -15 | E | = | | -11 | | (2) |
| | -54 | B | | -72 | C | | -78 | D | | -80 | E | = | | -68 | | (4) |
| -192 | B | | -240 | C | | -252 | D | | -255 | E | = | | -229 | | (5) |
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Multiply both sides of equation (2) by 27 Divide the two sides of equation (2) by 4, the equation can be obtained: | -54 | B | | -81 | C | | - | 189 2 | D | | - | 405 4 | E | = | | - | 297 4 | (9) | , then subtract both sides of equation (9) from both sides of equation (4), the equations are reduced to:
| | | | A | + | | B | + | | C | + | | D | + | | E | = | | 1 | | (1) |
| -8 | B | | -12 | C | | -14 | D | | -15 | E | = | | -11 | | (2) |
| | | 9 | C | + | | | 33 2 | D | + | | | 85 4 | E | = | | | 25 4 | | (4) |
| -192 | B | | -240 | C | | -252 | D | | -255 | E | = | | -229 | | (5) |
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Multiply both sides of equation (2) by 24, the equation can be obtained: | -192 | B | | -288 | C | | -336 | D | | -360 | E | = | | -264 | (10) | , then subtract both sides of equation (10) from both sides of equation (5), the equations are reduced to:
| | | | A | + | | B | + | | C | + | | D | + | | E | = | | 1 | | (1) |
| -8 | B | | -12 | C | | -14 | D | | -15 | E | = | | -11 | | (2) |
| | | 9 | C | + | | | 33 2 | D | + | | | 85 4 | E | = | | | 25 4 | | (4) |
| | 48 | C | + | | 84 | D | + | | 105 | E | = | | 35 | | (5) |
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交After the exchange of equation (3) and equation (4), the equation system becomes:
| | | | A | + | | B | + | | C | + | | D | + | | E | = | | 1 | | (1) |
| -8 | B | | -12 | C | | -14 | D | | -15 | E | = | | -11 | | (2) |
| | 9 | C | + | | | 33 2 | D | + | | | 85 4 | E | = | | | 25 4 | | (3) |
| | | 48 | C | + | | 84 | D | + | | 105 | E | = | | 35 | | (5) |
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Multiply both sides of equation (3) by 16 Divide the two sides of equation (3) by 3, the equation can be obtained: | | 48 | C | + | | 88 | D | + | | | 340 3 | E | = | | | 100 3 | (11) | , then subtract both sides of equation (11) from both sides of equation (5), the equations are reduced to:
| | | | A | + | | B | + | | C | + | | D | + | | E | = | | 1 | | (1) |
| -8 | B | | -12 | C | | -14 | D | | -15 | E | = | | -11 | | (2) |
| | 9 | C | + | | | 33 2 | D | + | | | 85 4 | E | = | | | 25 4 | | (3) |
| | |
交After the exchange of equation (4) and equation (5), the equation system becomes:
| | | | A | + | | B | + | | C | + | | D | + | | E | = | | 1 | | (1) |
| -8 | B | | -12 | C | | -14 | D | | -15 | E | = | | -11 | | (2) |
| | 9 | C | + | | | 33 2 | D | + | | | 85 4 | E | = | | | 25 4 | | (3) |
| | |
Multiply both sides of equation (5) by 25 Divide both sides of equation (5) by 3, get the equation:, then add the two sides of equation (12) to both sides of equation (4), get the equation:
| | | | A | + | | B | + | | C | + | | D | + | | E | = | | 1 | | (1) |
| -8 | B | | -12 | C | | -14 | D | | -15 | E | = | | -11 | | (2) |
| | 9 | C | + | | | 33 2 | D | + | | | 85 4 | E | = | | | 25 4 | | (3) |
| | |
Multiply both sides of equation (5) by 85 Divide both sides of equation (5) by 4, get the equation:, then subtract both sides of equation (13) from both sides of equation (3), get the equation:
| | | | A | + | | B | + | | C | + | | D | + | | E | = | | 1 | | (1) |
| -8 | B | | -12 | C | | -14 | D | | -15 | E | = | | -11 | | (2) |
| | | |
Multiply both sides of equation (5) by 15, get the equation:, then add the two sides of equation (14) to both sides of equation (2), get the equation:
| | | | A | + | | B | + | | C | + | | D | + | | E | = | | 1 | | (1) |
| | | | |
Subtract both sides of equation (5) from both sides of equation (1), get the equation:
Multiply both sides of equation (4) by 33 Divide both sides of equation (4) by 8, get the equation:, then add the two sides of equation (15) to both sides of equation (3), get the equation:
Multiply both sides of equation (4) by 7 Divide both sides of equation (4) by 2, get the equation:, then subtract both sides of equation (16) from both sides of equation (2), get the equation:
Divide both sides of equation (4) by 4, get the equation:, then add the two sides of equation (17) to both sides of equation (1), get the equation:
Multiply both sides of equation (3) by 4 Divide both sides of equation (3) by 3, get the equation:, then add the two sides of equation (18) to both sides of equation (2), get the equation:
Divide both sides of equation (3) by 9, get the equation:, then subtract both sides of equation (19) 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 (20) 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:
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》 |