详细信息: 输入的方程组为:
| | | | A | + | | B | + | | D | + | | E | + | | G | + | | H | + | | J | + | | K | = | | 200 | | (1) |
| | A | + | | C | + | | D | + | | F | + | | G | + | | I | + | | J | + | | L | = | | 180 | | (2) |
| | B | + | | C | + | | E | + | | F | + | | H | + | | I | + | | K | + | | L | = | | 160 | | (3) |
| | | | | | | | | | 解题过程:
用第 (2) 式两边同时 减去 第 (1) 等式两边,方程组化为:
| | | | A | + | | B | + | | D | + | | E | + | | G | + | | H | + | | J | + | | K | = | | 200 | | (1) |
| -1 | B | + | | C | | -1 | E | + | | F | | -1 | H | + | | I | | -1 | K | + | | L | = | | -20 | | (2) |
| | B | + | | C | + | | E | + | | F | + | | H | + | | I | + | | K | + | | L | = | | 160 | | (3) |
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用第 (3) 式两边同时 加上 第 (2) 等式两边,方程组化为:
| | | | A | + | | B | + | | D | + | | E | + | | G | + | | H | + | | J | + | | K | = | | 200 | | (1) |
| -1 | B | + | | C | | -1 | E | + | | F | | -1 | H | + | | I | | -1 | K | + | | L | = | | -20 | | (2) |
| | 2 | C | + | | 2 | F | + | | 2 | I | + | | 2 | L | = | | 140 | | (3) |
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将第 (3) 等式两边 除以2后,可以得到等式:,然后再同时用第 (2) 等式两边 减去 等式(13)两边,方程组化为:
| | | | A | + | | B | + | | D | + | | E | + | | G | + | | H | + | | J | + | | K | = | | 200 | | (1) |
| -1 | B | | -1 | E | | -1 | H | | -1 | K | = | | -90 | | (2) |
| | 2 | C | + | | 2 | F | + | | 2 | I | + | | 2 | L | = | | 140 | | (3) |
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用第 (1) 式两边同时 加上 第 (2) 等式两边,方程组化为:
| | | | -1 | B | | -1 | E | | -1 | H | | -1 | K | = | | -90 | | (2) |
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将未知数的系数化为1,方程组化为:
所以,方程组的解为:
其中: D, E, F, G, H, I, J, K, L 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》 |