detailed information: The input equation set is:
| | | | A | + | | C | + | | D | + | | F | + | | I | = | | 0 | | (1) |
| | | | | | | | | Question solving process:
Subtract both sides of equation (1) from both sides of equation (3) ,the equations are reduced to:
| | | | A | + | | C | + | | D | + | | F | + | | I | = | | 0 | | (1) |
| | | B | | -1 | C | | -1 | F | + | | G | | -1 | I | = | | 0 | | (3) |
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Subtract both sides of equation (1) from both sides of equation (4) ,the equations are reduced to:
| | | | A | + | | C | + | | D | + | | F | + | | I | = | | 0 | | (1) |
| | | B | | -1 | C | | -1 | F | + | | G | | -1 | I | = | | 0 | | (3) |
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Subtract both sides of equation (1) from both sides of equation (6) ,the equations are reduced to:
| | | | A | + | | C | + | | D | + | | F | + | | I | = | | 0 | | (1) |
| | | B | | -1 | C | | -1 | F | + | | G | | -1 | I | = | | 0 | | (3) |
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Subtract both sides of equation (1) from both sides of equation (9) ,the equations are reduced to:
| | | | A | + | | C | + | | D | + | | F | + | | I | = | | 0 | | (1) |
| | | B | | -1 | C | | -1 | F | + | | G | | -1 | I | = | | 0 | | (3) |
| | | | | | -1 | C | | -1 | D | + | | E | | -1 | F | + | | H | | -1 | I | = | | 1 | | (9) |
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Subtract both sides of equation (2) from both sides of equation (3) ,the equations are reduced to:
| | | | A | + | | C | + | | D | + | | F | + | | I | = | | 0 | | (1) |
| | -2 | C | | -1 | E | | -1 | F | + | | G | | -1 | H | | -1 | I | = | | 0 | | (3) |
| | | | | | -1 | C | | -1 | D | + | | E | | -1 | F | + | | H | | -1 | I | = | | 1 | | (9) |
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Subtract both sides of equation (2) from both sides of equation (5) ,the equations are reduced to:
| | | | A | + | | C | + | | D | + | | F | + | | I | = | | 0 | | (1) |
| | -2 | C | | -1 | E | | -1 | F | + | | G | | -1 | H | | -1 | I | = | | 0 | | (3) |
| | | | | | -1 | C | | -1 | D | + | | E | | -1 | F | + | | H | | -1 | I | = | | 1 | | (9) |
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Subtract both sides of equation (2) from both sides of equation (8) ,the equations are reduced to:
| | | | A | + | | C | + | | D | + | | F | + | | I | = | | 0 | | (1) |
| | -2 | C | | -1 | E | | -1 | F | + | | G | | -1 | H | | -1 | I | = | | 0 | | (3) |
| | | | | -1 | C | | -1 | E | + | | F | | -1 | H | + | | I | = | | 0 | | (8) |
| -1 | C | | -1 | D | + | | E | | -1 | F | + | | H | | -1 | I | = | | 1 | | (9) |
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Divide the two sides of equation (3) by 2, the equation can be obtained: | -1 | C | | - | 1 2 | E | | - | 1 2 | F | + | | | 1 2 | G | | - | 1 2 | H | | - | 1 2 | I | = | | 0 | (10) | , then subtract both sides of equation (10) from both sides of equation (5), the equations are reduced to:
| | | | A | + | | C | + | | D | + | | F | + | | I | = | | 0 | | (1) |
| | -2 | C | | -1 | E | | -1 | F | + | | G | | -1 | H | | -1 | I | = | | 0 | | (3) |
| | | | 1 2 | E | + | | | 1 2 | F | | - | 1 2 | G | | - | 1 2 | H | + | | | 3 2 | I | = | | 0 | | (5) |
| | | -1 | C | | -1 | E | + | | F | | -1 | H | + | | I | = | | 0 | | (8) |
| -1 | C | | -1 | D | + | | E | | -1 | F | + | | H | | -1 | I | = | | 1 | | (9) |
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Divide the two sides of equation (3) by 2, the equation can be obtained: | -1 | C | | - | 1 2 | E | | - | 1 2 | F | + | | | 1 2 | G | | - | 1 2 | H | | - | 1 2 | I | = | | 0 | (11) | , then subtract both sides of equation (11) from both sides of equation (6), the equations are reduced to:
| | | | A | + | | C | + | | D | + | | F | + | | I | = | | 0 | | (1) |
| | -2 | C | | -1 | E | | -1 | F | + | | G | | -1 | H | | -1 | I | = | | 0 | | (3) |
| | | | 1 2 | E | + | | | 1 2 | F | | - | 1 2 | G | | - | 1 2 | H | + | | | 3 2 | I | = | | 0 | | (5) |
| | | 1 2 | E | | - | 1 2 | F | | - | 1 2 | G | + | | | 3 2 | H | | - | 1 2 | I | = | | 0 | | (6) |
| | -1 | C | | -1 | E | + | | F | | -1 | H | + | | I | = | | 0 | | (8) |
| -1 | C | | -1 | D | + | | E | | -1 | F | + | | H | | -1 | I | = | | 1 | | (9) |
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Divide the two sides of equation (3) by 2, the equation can be obtained: | -1 | C | | - | 1 2 | E | | - | 1 2 | F | + | | | 1 2 | G | | - | 1 2 | H | | - | 1 2 | I | = | | 0 | (12) | , then add the two sides of equation (12) to both sides of equation (7), the equations are reduced to:
| | | | A | + | | C | + | | D | + | | F | + | | I | = | | 0 | | (1) |
| | -2 | C | | -1 | E | | -1 | F | + | | G | | -1 | H | | -1 | I | = | | 0 | | (3) |
| | | | 1 2 | E | + | | | 1 2 | F | | - | 1 2 | G | | - | 1 2 | H | + | | | 3 2 | I | = | | 0 | | (5) |
| | | 1 2 | E | | - | 1 2 | F | | - | 1 2 | G | + | | | 3 2 | H | | - | 1 2 | I | = | | 0 | | (6) |
| - | 1 2 | E | | - | 1 2 | F | + | | | 3 2 | G | | - | 1 2 | H | | - | 1 2 | I | = | | 1 | | (7) |
| -1 | C | | -1 | E | + | | F | | -1 | H | + | | I | = | | 0 | | (8) |
| -1 | C | | -1 | D | + | | E | | -1 | F | + | | H | | -1 | I | = | | 1 | | (9) |
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Divide the two sides of equation (3) by 2, the equation can be obtained: | -1 | C | | - | 1 2 | E | | - | 1 2 | F | + | | | 1 2 | G | | - | 1 2 | H | | - | 1 2 | I | = | | 0 | (13) | , then subtract both sides of equation (13) from both sides of equation (8), the equations are reduced to:
| | | | A | + | | C | + | | D | + | | F | + | | I | = | | 0 | | (1) |
| | -2 | C | | -1 | E | | -1 | F | + | | G | | -1 | H | | -1 | I | = | | 0 | | (3) |
| | | | 1 2 | E | + | | | 1 2 | F | | - | 1 2 | G | | - | 1 2 | H | + | | | 3 2 | I | = | | 0 | | (5) |
| | | 1 2 | E | | - | 1 2 | F | | - | 1 2 | G | + | | | 3 2 | H | | - | 1 2 | I | = | | 0 | | (6) |
| - | 1 2 | E | | - | 1 2 | F | + | | | 3 2 | G | | - | 1 2 | H | | - | 1 2 | I | = | | 1 | | (7) |
| - | 1 2 | E | + | | | 3 2 | F | | - | 1 2 | G | | - | 1 2 | H | + | | | 3 2 | I | = | | 0 | | (8) |
| -1 | C | | -1 | D | + | | E | | -1 | F | + | | H | | -1 | I | = | | 1 | | (9) |
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Divide the two sides of equation (3) by 2, the equation can be obtained: | -1 | C | | - | 1 2 | E | | - | 1 2 | F | + | | | 1 2 | G | | - | 1 2 | H | | - | 1 2 | I | = | | 0 | (14) | , then subtract both sides of equation (14) from both sides of equation (9), the equations are reduced to:
| | | | A | + | | C | + | | D | + | | F | + | | I | = | | 0 | | (1) |
| | -2 | C | | -1 | E | | -1 | F | + | | G | | -1 | H | | -1 | I | = | | 0 | | (3) |
| | | | 1 2 | E | + | | | 1 2 | F | | - | 1 2 | G | | - | 1 2 | H | + | | | 3 2 | I | = | | 0 | | (5) |
| | | 1 2 | E | | - | 1 2 | F | | - | 1 2 | G | + | | | 3 2 | H | | - | 1 2 | I | = | | 0 | | (6) |
| - | 1 2 | E | | - | 1 2 | F | + | | | 3 2 | G | | - | 1 2 | H | | - | 1 2 | I | = | | 1 | | (7) |
| - | 1 2 | E | + | | | 3 2 | F | | - | 1 2 | G | | - | 1 2 | H | + | | | 3 2 | I | = | | 0 | | (8) |
| -1 | D | + | | | 3 2 | E | | - | 1 2 | F | | - | 1 2 | G | + | | | 3 2 | H | | - | 1 2 | I | = | | 1 | | (9) |
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Subtract both sides of equation (4) from both sides of equation (9) ,the equations are reduced to:
| | | | A | + | | C | + | | D | + | | F | + | | I | = | | 0 | | (1) |
| | -2 | C | | -1 | E | | -1 | F | + | | G | | -1 | H | | -1 | I | = | | 0 | | (3) |
| | | | 1 2 | E | + | | | 1 2 | F | | - | 1 2 | G | | - | 1 2 | H | + | | | 3 2 | I | = | | 0 | | (5) |
| | | 1 2 | E | | - | 1 2 | F | | - | 1 2 | G | + | | | 3 2 | H | | - | 1 2 | I | = | | 0 | | (6) |
| - | 1 2 | E | | - | 1 2 | F | + | | | 3 2 | G | | - | 1 2 | H | | - | 1 2 | I | = | | 1 | | (7) |
| - | 1 2 | E | + | | | 3 2 | F | | - | 1 2 | G | | - | 1 2 | H | + | | | 3 2 | I | = | | 0 | | (8) |
| | | 3 2 | E | | - | 1 2 | F | | - | 1 2 | G | + | | | 3 2 | H | + | | | 1 2 | I | = | | 0 | | (9) |
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Subtract both sides of equation (5) from both sides of equation (6) ,the equations are reduced to:
| | | | A | + | | C | + | | D | + | | F | + | | I | = | | 0 | | (1) |
| | -2 | C | | -1 | E | | -1 | F | + | | G | | -1 | H | | -1 | I | = | | 0 | | (3) |
| | | | 1 2 | E | + | | | 1 2 | F | | - | 1 2 | G | | - | 1 2 | H | + | | | 3 2 | I | = | | 0 | | (5) |
| | - | 1 2 | E | | - | 1 2 | F | + | | | 3 2 | G | | - | 1 2 | H | | - | 1 2 | I | = | | 1 | | (7) |
| - | 1 2 | E | + | | | 3 2 | F | | - | 1 2 | G | | - | 1 2 | H | + | | | 3 2 | I | = | | 0 | | (8) |
| | | 3 2 | E | | - | 1 2 | F | | - | 1 2 | G | + | | | 3 2 | H | + | | | 1 2 | I | = | | 0 | | (9) |
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Add both sides of equation (5) to both sides of equation (7) ,the equations are reduced to:
| | | | A | + | | C | + | | D | + | | F | + | | I | = | | 0 | | (1) |
| | -2 | C | | -1 | E | | -1 | F | + | | G | | -1 | H | | -1 | I | = | | 0 | | (3) |
| | | | 1 2 | E | + | | | 1 2 | F | | - | 1 2 | G | | - | 1 2 | H | + | | | 3 2 | I | = | | 0 | | (5) |
| | | - | 1 2 | E | + | | | 3 2 | F | | - | 1 2 | G | | - | 1 2 | H | + | | | 3 2 | I | = | | 0 | | (8) |
| | | 3 2 | E | | - | 1 2 | F | | - | 1 2 | G | + | | | 3 2 | H | + | | | 1 2 | I | = | | 0 | | (9) |
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Add both sides of equation (5) to both sides of equation (8) ,the equations are reduced to:
| | | | A | + | | C | + | | D | + | | F | + | | I | = | | 0 | | (1) |
| | -2 | C | | -1 | E | | -1 | F | + | | G | | -1 | H | | -1 | I | = | | 0 | | (3) |
| | | | 1 2 | E | + | | | 1 2 | F | | - | 1 2 | G | | - | 1 2 | H | + | | | 3 2 | I | = | | 0 | | (5) |
| | | | | | 3 2 | E | | - | 1 2 | F | | - | 1 2 | G | + | | | 3 2 | H | + | | | 1 2 | I | = | | 0 | | (9) |
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Multiply both sides of equation (5) by 3, the equation can be obtained: | | | 3 2 | E | + | | | 3 2 | F | | - | 3 2 | G | | - | 3 2 | H | + | | | 9 2 | I | = | | 0 | (15) | , then subtract both sides of equation (15) from both sides of equation (9), the equations are reduced to:
| | | | A | + | | C | + | | D | + | | F | + | | I | = | | 0 | | (1) |
| | -2 | C | | -1 | E | | -1 | F | + | | G | | -1 | H | | -1 | I | = | | 0 | | (3) |
| | | | 1 2 | E | + | | | 1 2 | F | | - | 1 2 | G | | - | 1 2 | H | + | | | 3 2 | I | = | | 0 | | (5) |
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Multiply both sides of equation (6) by 2, the equation can be obtained: , then add the two sides of equation (16) to both sides of equation (8), the equations are reduced to:
| | | | A | + | | C | + | | D | + | | F | + | | I | = | | 0 | | (1) |
| | -2 | C | | -1 | E | | -1 | F | + | | G | | -1 | H | | -1 | I | = | | 0 | | (3) |
| | | | 1 2 | E | + | | | 1 2 | F | | - | 1 2 | G | | - | 1 2 | H | + | | | 3 2 | I | = | | 0 | | (5) |
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Multiply both sides of equation (6) by 2, the equation can be obtained: , then subtract both sides of equation (17) from both sides of equation (9), the equations are reduced to:
| | | | A | + | | C | + | | D | + | | F | + | | I | = | | 0 | | (1) |
| | -2 | C | | -1 | E | | -1 | F | + | | G | | -1 | H | | -1 | I | = | | 0 | | (3) |
| | | | 1 2 | E | + | | | 1 2 | F | | - | 1 2 | G | | - | 1 2 | H | + | | | 3 2 | I | = | | 0 | | (5) |
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Add both sides of equation (7) to both sides of equation (8) ,the equations are reduced to:
| | | | A | + | | C | + | | D | + | | F | + | | I | = | | 0 | | (1) |
| | -2 | C | | -1 | E | | -1 | F | + | | G | | -1 | H | | -1 | I | = | | 0 | | (3) |
| | | | 1 2 | E | + | | | 1 2 | F | | - | 1 2 | G | | - | 1 2 | H | + | | | 3 2 | I | = | | 0 | | (5) |
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Subtract both sides of equation (7) from both sides of equation (9) ,the equations are reduced to:
| | | | A | + | | C | + | | D | + | | F | + | | I | = | | 0 | | (1) |
| | -2 | C | | -1 | E | | -1 | F | + | | G | | -1 | H | | -1 | I | = | | 0 | | (3) |
| | | | 1 2 | E | + | | | 1 2 | F | | - | 1 2 | G | | - | 1 2 | H | + | | | 3 2 | I | = | | 0 | | (5) |
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Add both sides of equation (9) to both sides of equation (7), get the equation:
| | | | A | + | | C | + | | D | + | | F | + | | I | = | | 0 | | (1) |
| | -2 | C | | -1 | E | | -1 | F | + | | G | | -1 | H | | -1 | I | = | | 0 | | (3) |
| | | | 1 2 | E | + | | | 1 2 | F | | - | 1 2 | G | | - | 1 2 | H | + | | | 3 2 | I | = | | 0 | | (5) |
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Multiply both sides of equation (9) by 2, get the equation:, then subtract both sides of equation (18) from both sides of equation (6), get the equation:
| | | | A | + | | C | + | | D | + | | F | + | | I | = | | 0 | | (1) |
| | -2 | C | | -1 | E | | -1 | F | + | | G | | -1 | H | | -1 | I | = | | 0 | | (3) |
| | | | 1 2 | E | + | | | 1 2 | F | | - | 1 2 | G | | - | 1 2 | H | + | | | 3 2 | I | = | | 0 | | (5) |
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Multiply both sides of equation (9) by 3 Divide both sides of equation (9) by 2, get the equation:, then add the two sides of equation (19) to both sides of equation (5), get the equation:
| | | | A | + | | C | + | | D | + | | F | + | | I | = | | 0 | | (1) |
| | -2 | C | | -1 | E | | -1 | F | + | | G | | -1 | H | | -1 | I | = | | 0 | | (3) |
| | | | 1 2 | E | + | | | 1 2 | F | | - | 1 2 | G | | - | 1 2 | H | = | | - | 3 2 | | (5) |
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Subtract both sides of equation (9) from both sides of equation (4), get the equation:
| | | | A | + | | C | + | | D | + | | F | + | | I | = | | 0 | | (1) |
| | -2 | C | | -1 | E | | -1 | F | + | | G | | -1 | H | | -1 | I | = | | 0 | | (3) |
| | | | 1 2 | E | + | | | 1 2 | F | | - | 1 2 | G | | - | 1 2 | H | = | | - | 3 2 | | (5) |
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Subtract both sides of equation (9) from both sides of equation (3), get the equation:
| | | | A | + | | C | + | | D | + | | F | + | | I | = | | 0 | | (1) |
| | -2 | C | | -1 | E | | -1 | F | + | | G | | -1 | H | = | | 1 | | (3) |
| | | | 1 2 | E | + | | | 1 2 | F | | - | 1 2 | G | | - | 1 2 | H | = | | - | 3 2 | | (5) |
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Add both sides of equation (9) to both sides of equation (1), get the equation:
| | | | | -2 | C | | -1 | E | | -1 | F | + | | G | | -1 | H | = | | 1 | | (3) |
| | | | 1 2 | E | + | | | 1 2 | F | | - | 1 2 | G | | - | 1 2 | H | = | | - | 3 2 | | (5) |
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Divide both sides of equation (8) by 2, get the equation:, then add the two sides of equation (20) to both sides of equation (7), get the equation:
| | | | | -2 | C | | -1 | E | | -1 | F | + | | G | | -1 | H | = | | 1 | | (3) |
| | | | 1 2 | E | + | | | 1 2 | F | | - | 1 2 | G | | - | 1 2 | H | = | | - | 3 2 | | (5) |
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Subtract both sides of equation (8) from both sides of equation (6), get the equation:
| | | | | -2 | C | | -1 | E | | -1 | F | + | | G | | -1 | H | = | | 1 | | (3) |
| | | | 1 2 | E | + | | | 1 2 | F | | - | 1 2 | G | | - | 1 2 | H | = | | - | 3 2 | | (5) |
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Divide both sides of equation (8) by 4, get the equation:, then add the two sides of equation (21) to both sides of equation (5), get the equation:
| | | | | -2 | C | | -1 | E | | -1 | F | + | | G | | -1 | H | = | | 1 | | (3) |
| | | | 1 2 | E | + | | | 1 2 | F | | - | 1 2 | G | = | | - | 5 4 | | (5) |
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Divide both sides of equation (8) by 2, get the equation:, then add the two sides of equation (22) to both sides of equation (3), get the equation:
| | | | | | | | | 1 2 | E | + | | | 1 2 | F | | - | 1 2 | G | = | | - | 5 4 | | (5) |
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Divide both sides of equation (8) by 2, get the equation:, then subtract both sides of equation (23) from both sides of equation (2), get the equation:
| | | | | | | | | 1 2 | E | + | | | 1 2 | F | | - | 1 2 | G | = | | - | 5 4 | | (5) |
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Divide both sides of equation (7) by 2, get the equation:, then add the two sides of equation (24) to both sides of equation (5), get the equation:
Subtract both sides of equation (7) from both sides of equation (3), get the equation:
Divide both sides of equation (6) by 2, get the equation:, then add the two sides of equation (25) to both sides of equation (5), get the equation:
Subtract both sides of equation (6) from both sides of equation (3), get the equation:
Add both sides of equation (6) to both sides of equation (1), get the equation:
Multiply both sides of equation (5) by 2, get the equation:, then add the two sides of equation (26) to both sides of equation (3), get the equation:
Multiply both sides of equation (5) by 2, get the equation:, then subtract both sides of equation (27) 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 (28) to both sides of equation (2), get the equation:
Divide both sides of equation (3) by 2, get the equation:, then add the two sides of equation (29) 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》 |