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