detailed information: The input equation set is:
| | | | A | + | | B | + | | C | + | | D | + | | E | = | | 0 | | (1) |
| | | 16 | A | + | | 8 | B | + | | 4 | C | + | | 2 | D | + | | E | = | | 1 | | (3) |
| | 32 | A | + | | 12 | B | + | | 4 | C | + | | D | = | | 0 | | (4) |
| | Question solving process:
Multiply both sides of equation (1) by 4, the equation can be obtained: | | 4 | A | + | | 4 | B | + | | 4 | C | + | | 4 | D | + | | 4 | E | = | | 0 | (6) | , then subtract both sides of equation (6) from both sides of equation (2), the equations are reduced to:
| | | | A | + | | B | + | | C | + | | D | + | | E | = | | 0 | | (1) |
| | | 16 | A | + | | 8 | B | + | | 4 | C | + | | 2 | D | + | | E | = | | 1 | | (3) |
| | 32 | A | + | | 12 | B | + | | 4 | C | + | | D | = | | 0 | | (4) |
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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 | = | | 0 | (7) | , then subtract both sides of equation (7) from both sides of equation (3), the equations are reduced to:
| | | | A | + | | B | + | | C | + | | D | + | | E | = | | 0 | | (1) |
| | -8 | B | | -12 | C | | -14 | D | | -15 | E | = | | 1 | | (3) |
| | 32 | A | + | | 12 | B | + | | 4 | C | + | | D | = | | 0 | | (4) |
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Multiply both sides of equation (1) by 32, the equation can be obtained: | | 32 | A | + | | 32 | B | + | | 32 | C | + | | 32 | D | + | | 32 | E | = | | 0 | (8) | , then subtract both sides of equation (8) from both sides of equation (4), the equations are reduced to:
| | | | A | + | | B | + | | C | + | | D | + | | E | = | | 0 | | (1) |
| | -8 | B | | -12 | C | | -14 | D | | -15 | E | = | | 1 | | (3) |
| -20 | B | | -28 | C | | -31 | D | | -32 | E | = | | 0 | | (4) |
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Multiply both sides of equation (1) by 48, the equation can be obtained: | | 48 | A | + | | 48 | B | + | | 48 | C | + | | 48 | D | + | | 48 | E | = | | 0 | (9) | , then subtract both sides of equation (9) from both sides of equation (5), the equations are reduced to:
| | | | A | + | | B | + | | C | + | | D | + | | E | = | | 0 | | (1) |
| | -8 | B | | -12 | C | | -14 | D | | -15 | E | = | | 1 | | (3) |
| -20 | B | | -28 | C | | -31 | D | | -32 | E | = | | 0 | | (4) |
| -36 | B | | -46 | C | | -48 | D | | -48 | E | = | | 0 | | (5) |
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Multiply both sides of equation (2) by 8, the equation can be obtained: | -8 | B | | -16 | C | | -24 | D | | -32 | E | = | | 0 | (10) | , then subtract both sides of equation (10) from both sides of equation (3), the equations are reduced to:
| | | | A | + | | B | + | | C | + | | D | + | | E | = | | 0 | | (1) |
| | | -20 | B | | -28 | C | | -31 | D | | -32 | E | = | | 0 | | (4) |
| -36 | B | | -46 | C | | -48 | D | | -48 | E | = | | 0 | | (5) |
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Multiply both sides of equation (2) by 20, the equation can be obtained: | -20 | B | | -40 | C | | -60 | D | | -80 | E | = | | 0 | (11) | , then subtract both sides of equation (11) from both sides of equation (4), the equations are reduced to:
| | | | A | + | | B | + | | C | + | | D | + | | E | = | | 0 | | (1) |
| | | | -36 | B | | -46 | C | | -48 | D | | -48 | E | = | | 0 | | (5) |
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Multiply both sides of equation (2) by 36, the equation can be obtained: | -36 | B | | -72 | C | | -108 | D | | -144 | E | = | | 0 | (12) | , then subtract both sides of equation (12) from both sides of equation (5), the equations are reduced to:
| | | | A | + | | B | + | | C | + | | D | + | | E | = | | 0 | | (1) |
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Multiply both sides of equation (3) by 3, the equation can be obtained: , then subtract both sides of equation (13) from both sides of equation (4), the equations are reduced to:
| | | | A | + | | B | + | | C | + | | D | + | | E | = | | 0 | | (1) |
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Multiply both sides of equation (3) by 13 Divide the two sides of equation (3) by 2, the equation can be obtained: | | 26 | C | + | | 65 | D | + | | | 221 2 | E | = | | | 13 2 | (14) | , then subtract both sides of equation (14) from both sides of equation (5), the equations are reduced to:
| | | | A | + | | B | + | | C | + | | D | + | | E | = | | 0 | | (1) |
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Multiply both sides of equation (4) by 5, the equation can be obtained: , then subtract both sides of equation (15) from both sides of equation (5), the equations are reduced to:
| | | | A | + | | B | + | | C | + | | D | + | | E | = | | 0 | | (1) |
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Multiply both sides of equation (5) by 6, get the equation:, then add the two sides of equation (16) to both sides of equation (4), get the equation:
| | | | A | + | | B | + | | C | + | | D | + | | E | = | | 0 | | (1) |
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Multiply both sides of equation (5) by 34, get the equation:, then subtract both sides of equation (17) from both sides of equation (3), get the equation:
| | | | A | + | | B | + | | C | + | | D | + | | E | = | | 0 | | (1) |
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Multiply both sides of equation (5) by 8, get the equation:, then add the two sides of equation (18) to both sides of equation (2), get the equation:
| | | | A | + | | B | + | | C | + | | D | + | | E | = | | 0 | | (1) |
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Multiply both sides of equation (5) by 2, get the equation:, then subtract both sides of equation (19) from both sides of equation (1), get the equation:
Multiply both sides of equation (4) by 10, get the equation:, then add the two sides of equation (20) to both sides of equation (3), get the equation:
Multiply both sides of equation (4) by 3, get the equation:, then subtract both sides of equation (21) from both sides of equation (2), get the equation:
Add both sides of equation (4) to both sides of equation (1), get the equation:
Divide both sides of equation (3) by 2, get the equation:, then add the two sides of equation (22) to both sides of equation (2), get the equation:
Divide both sides of equation (3) by 4, get the equation:, then subtract both sides of equation (23) 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》 |