详细信息: 输入的方程组为:
| | | | 3 | A | + | | B | | -8 | C | + | | 2 | D | + | | E | = | | 0 | | (1) |
| | 2 | A | | -2 | B | | -3 | C | | -7 | D | + | | 2 | E | = | | 0 | | (2) |
| | A | + | | 11 | B | | -12 | C | + | | 34 | D | | -5 | E | = | | 0 | | (3) |
| | A | | -5 | B | + | | 2 | C | | -16 | D | + | | 3 | E | = | | 0 | | (4) |
| | 解题过程:
将第 (1) 等式两边 乘以2 除以3后,可以得到等式: | | 2 | A | + | | | 2 3 | B | | - | 16 3 | C | + | | | 4 3 | D | + | | | 2 3 | E | = | | 0 | (6) | ,然后再同时用第 (2) 等式两边 减去 等式(6)两边,方程组化为:
| | | | 3 | A | + | | B | | -8 | C | + | | 2 | D | + | | E | = | | 0 | | (1) |
| - | 8 3 | B | + | | | 7 3 | C | | - | 25 3 | D | + | | | 4 3 | E | = | | 0 | | (2) |
| | A | + | | 11 | B | | -12 | C | + | | 34 | D | | -5 | E | = | | 0 | | (3) |
| | A | | -5 | B | + | | 2 | C | | -16 | D | + | | 3 | E | = | | 0 | | (4) |
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将第 (1) 等式两边 除以3后,可以得到等式: | | A | + | | | 1 3 | B | | - | 8 3 | C | + | | | 2 3 | D | + | | | 1 3 | E | = | | 0 | (7) | ,然后再同时用第 (3) 等式两边 减去 等式(7)两边,方程组化为:
| | | | 3 | A | + | | B | | -8 | C | + | | 2 | D | + | | E | = | | 0 | | (1) |
| - | 8 3 | B | + | | | 7 3 | C | | - | 25 3 | D | + | | | 4 3 | E | = | | 0 | | (2) |
| | | 32 3 | B | | - | 28 3 | C | + | | | 100 3 | D | | - | 16 3 | E | = | | 0 | | (3) |
| | A | | -5 | B | + | | 2 | C | | -16 | D | + | | 3 | E | = | | 0 | | (4) |
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将第 (1) 等式两边 除以3后,可以得到等式: | | A | + | | | 1 3 | B | | - | 8 3 | C | + | | | 2 3 | D | + | | | 1 3 | E | = | | 0 | (8) | ,然后再同时用第 (4) 等式两边 减去 等式(8)两边,方程组化为:
| | | | 3 | A | + | | B | | -8 | C | + | | 2 | D | + | | E | = | | 0 | | (1) |
| - | 8 3 | B | + | | | 7 3 | C | | - | 25 3 | D | + | | | 4 3 | E | = | | 0 | | (2) |
| | | 32 3 | B | | - | 28 3 | C | + | | | 100 3 | D | | - | 16 3 | E | = | | 0 | | (3) |
| - | 16 3 | B | + | | | 14 3 | C | | - | 50 3 | D | + | | | 8 3 | E | = | | 0 | | (4) |
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将第 (2) 等式两边 乘以4后,可以得到等式: | - | 32 3 | B | + | | | 28 3 | C | | - | 100 3 | D | + | | | 16 3 | E | = | | 0 | (9) | ,然后再同时用第 (3) 等式两边 加上 等式(9)两边,方程组化为:
| | | | 3 | A | + | | B | | -8 | C | + | | 2 | D | + | | E | = | | 0 | | (1) |
| - | 8 3 | B | + | | | 7 3 | C | | - | 25 3 | D | + | | | 4 3 | E | = | | 0 | | (2) |
| | - | 16 3 | B | + | | | 14 3 | C | | - | 50 3 | D | + | | | 8 3 | E | = | | 0 | | (4) |
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将第 (2) 等式两边 乘以2后,可以得到等式: | - | 16 3 | B | + | | | 14 3 | C | | - | 50 3 | D | + | | | 8 3 | E | = | | 0 | (10) | ,然后再同时用第 (4) 等式两边 减去 等式(10)两边,方程组化为:
| | | | 3 | A | + | | B | | -8 | C | + | | 2 | D | + | | E | = | | 0 | | (1) |
| - | 8 3 | B | + | | | 7 3 | C | | - | 25 3 | D | + | | | 4 3 | E | = | | 0 | | (2) |
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将第 (2) 等式两边 乘以3 除以8后,可以得到等式: | -1 | B | + | | | 7 8 | C | | - | 25 8 | D | + | | | 1 2 | E | = | | 0 | (11) | ,然后再同时用第 (1) 等式两边 加上 等式(11)两边,方程组化为:
| | | | 3 | A | | - | 57 8 | C | | - | 9 8 | D | + | | | 3 2 | E | = | | 0 | | (1) |
| - | 8 3 | B | + | | | 7 3 | C | | - | 25 3 | D | + | | | 4 3 | E | = | | 0 | | (2) |
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将未知数的系数化为1,方程组化为:
| | | | A | | - | 19 8 | C | | - | 3 8 | D | + | | | 1 2 | E | = | | 0 | | (1) |
| | B | | - | 7 8 | C | + | | | 25 8 | D | | - | 1 2 | E | = | | 0 | | (2) |
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所以,方程组的解为:
其中: C, D, E 为任意常数。 解方程组的详细方法请参阅:《多元一次方程组的解法》 |