线性代数 示例

求秩 [[2,-1,-1,5],[-1,1,2,-3],[1,-2,3,4]]
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
Multiply each element of by to make the entry at a .
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解题步骤 1.4.1
Multiply each element of by to make the entry at a .
解题步骤 1.4.2
化简
解题步骤 1.5
Perform the row operation to make the entry at a .
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解题步骤 1.5.1
Perform the row operation to make the entry at a .
解题步骤 1.5.2
化简
解题步骤 1.6
Multiply each element of by to make the entry at a .
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解题步骤 1.6.1
Multiply each element of by 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
Perform the row operation to make the entry at a .
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解题步骤 1.8.1
Perform the row operation to make the entry at a .
解题步骤 1.8.2
化简
解题步骤 1.9
Perform the row operation to make the entry at a .
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解题步骤 1.9.1
Perform the row operation to make the entry at a .
解题步骤 1.9.2
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
解题步骤 3
The rank is the number of pivot columns.