线性代数 示例

求枢轴位置(主元位置)和主列 [[-2,-5,8,0,17,0],[1,3,-5,1,5,0],[3,11,-19,7,1,0],[1,7,-13,5,-3,0]]
解题步骤 1
求行简化阶梯形矩阵。
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解题步骤 1.1
Multiply each element of by to make the entry at a .
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解题步骤 1.1.1
Multiply each element of by to make the entry at a .
解题步骤 1.1.2
化简
解题步骤 1.2
Perform the row operation to make the entry at a .
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解题步骤 1.2.1
Perform the row operation to make the entry at a .
解题步骤 1.2.2
化简
解题步骤 1.3
Perform the row operation to make the entry at a .
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解题步骤 1.3.1
Perform the row operation to make the entry at a .
解题步骤 1.3.2
化简
解题步骤 1.4
Perform the row operation to make the entry at a .
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解题步骤 1.4.1
Perform the row operation to make the entry at a .
解题步骤 1.4.2
化简
解题步骤 1.5
Multiply each element of by to make the entry at a .
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解题步骤 1.5.1
Multiply each element of by to make the entry at a .
解题步骤 1.5.2
化简
解题步骤 1.6
Perform the row operation to make the entry at a .
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解题步骤 1.6.1
Perform the row operation to make the entry at a .
解题步骤 1.6.2
化简
解题步骤 1.7
Perform the row operation to make the entry at a .
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解题步骤 1.7.1
Perform the row operation to make the entry at a .
解题步骤 1.7.2
化简
解题步骤 1.8
Swap with to put a nonzero entry at .
解题步骤 1.9
Multiply each element of by to make the entry at a .
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解题步骤 1.9.1
Multiply each element of by to make the entry at a .
解题步骤 1.9.2
化简
解题步骤 1.10
Multiply each element of by to make the entry at a .
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解题步骤 1.10.1
Multiply each element of by to make the entry at a .
解题步骤 1.10.2
化简
解题步骤 1.11
Perform the row operation to make the entry at a .
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解题步骤 1.11.1
Perform the row operation to make the entry at a .
解题步骤 1.11.2
化简
解题步骤 1.12
Perform the row operation to make the entry at a .
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解题步骤 1.12.1
Perform the row operation to make the entry at a .
解题步骤 1.12.2
化简
解题步骤 1.13
Perform the row operation to make the entry at a .
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解题步骤 1.13.1
Perform the row operation to make the entry at a .
解题步骤 1.13.2
化简
解题步骤 1.14
Perform the row operation to make the entry at a .
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解题步骤 1.14.1
Perform the row operation to make the entry at a .
解题步骤 1.14.2
化简
解题步骤 1.15
Perform the row operation to make the entry at a .
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解题步骤 1.15.1
Perform the row operation to make the entry at a .
解题步骤 1.15.2
化简
解题步骤 2
The pivot positions are the locations with the leading in each row. The pivot columns are the columns that have a pivot position.
Pivot Positions: and
Pivot Columns: and