线性代数 示例

表示为向量等式 x+2y=48 , x+y=30 , 2x+y=50 , f=70x+30y
, , ,
解题步骤 1
将所有包含变量的项移到等式左边。
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解题步骤 1.1
从等式两边同时减去
解题步骤 1.2
从等式两边同时减去
解题步骤 2
以矩阵形式书写方程组。
解题步骤 3
求行简化阶梯形矩阵。
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解题步骤 3.1
Swap with to put a nonzero entry at .
解题步骤 3.2
Perform the row operation to make the entry at a .
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解题步骤 3.2.1
Perform the row operation to make the entry at a .
解题步骤 3.2.2
化简
解题步骤 3.3
Perform the row operation to make the entry at a .
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解题步骤 3.3.1
Perform the row operation to make the entry at a .
解题步骤 3.3.2
化简
解题步骤 3.4
Multiply each element of by to make the entry at a .
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解题步骤 3.4.1
Multiply each element of by to make the entry at a .
解题步骤 3.4.2
化简
解题步骤 3.5
Perform the row operation to make the entry at a .
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解题步骤 3.5.1
Perform the row operation to make the entry at a .
解题步骤 3.5.2
化简
解题步骤 3.6
Multiply each element of by to make the entry at a .
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解题步骤 3.6.1
Multiply each element of by to make the entry at a .
解题步骤 3.6.2
化简
解题步骤 3.7
Perform the row operation to make the entry at a .
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解题步骤 3.7.1
Perform the row operation to make the entry at a .
解题步骤 3.7.2
化简
解题步骤 3.8
Perform the row operation to make the entry at a .
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解题步骤 3.8.1
Perform the row operation to make the entry at a .
解题步骤 3.8.2
化简
解题步骤 3.9
Perform the row operation to make the entry at a .
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解题步骤 3.9.1
Perform the row operation to make the entry at a .
解题步骤 3.9.2
化简
解题步骤 3.10
Perform the row operation to make the entry at a .
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解题步骤 3.10.1
Perform the row operation to make the entry at a .
解题步骤 3.10.2
化简
解题步骤 3.11
Perform the row operation to make the entry at a .
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解题步骤 3.11.1
Perform the row operation to make the entry at a .
解题步骤 3.11.2
化简
解题步骤 4
使用结果矩阵定义方程组的最终解。
解题步骤 5
因为 ,所以没有解。
无解