线性代数 示例

求出零度 [[14,-18,-8,10,6,-6,-14],[-8,12,14,-4,-12,-10,10],[10,-14,-12,10,-12,4,16],[-6,10,16,-2,-14,-8,16],[12,-16,-10,8,8,18,6]]
解题步骤 1
Nullity is the dimension of the null space, which is the same as the number of free variables in the system after row reducing. The free variables are the columns without pivot positions.
解题步骤 2
求行简化阶梯形矩阵。
点击获取更多步骤...
解题步骤 2.1
Multiply each element of by to make the entry at a .
点击获取更多步骤...
解题步骤 2.1.1
Multiply each element of by to make the entry at a .
解题步骤 2.1.2
化简
解题步骤 2.2
Perform the row operation to make the entry at a .
点击获取更多步骤...
解题步骤 2.2.1
Perform the row operation to make the entry at a .
解题步骤 2.2.2
化简
解题步骤 2.3
Perform the row operation to make the entry at a .
点击获取更多步骤...
解题步骤 2.3.1
Perform the row operation to make the entry at a .
解题步骤 2.3.2
化简
解题步骤 2.4
Perform the row operation to make the entry at a .
点击获取更多步骤...
解题步骤 2.4.1
Perform the row operation to make the entry at a .
解题步骤 2.4.2
化简
解题步骤 2.5
Perform the row operation to make the entry at a .
点击获取更多步骤...
解题步骤 2.5.1
Perform the row operation to make the entry at a .
解题步骤 2.5.2
化简
解题步骤 2.6
Multiply each element of by to make the entry at a .
点击获取更多步骤...
解题步骤 2.6.1
Multiply each element of by to make the entry at a .
解题步骤 2.6.2
化简
解题步骤 2.7
Perform the row operation to make the entry at a .
点击获取更多步骤...
解题步骤 2.7.1
Perform the row operation to make the entry at a .
解题步骤 2.7.2
化简
解题步骤 2.8
Perform the row operation to make the entry at a .
点击获取更多步骤...
解题步骤 2.8.1
Perform the row operation to make the entry at a .
解题步骤 2.8.2
化简
解题步骤 2.9
Perform the row operation to make the entry at a .
点击获取更多步骤...
解题步骤 2.9.1
Perform the row operation to make the entry at a .
解题步骤 2.9.2
化简
解题步骤 2.10
Multiply each element of by to make the entry at a .
点击获取更多步骤...
解题步骤 2.10.1
Multiply each element of by to make the entry at a .
解题步骤 2.10.2
化简
解题步骤 2.11
Multiply each element of by to make the entry at a .
点击获取更多步骤...
解题步骤 2.11.1
Multiply each element of by to make the entry at a .
解题步骤 2.11.2
化简
解题步骤 2.12
Perform the row operation to make the entry at a .
点击获取更多步骤...
解题步骤 2.12.1
Perform the row operation to make the entry at a .
解题步骤 2.12.2
化简
解题步骤 2.13
Perform the row operation to make the entry at a .
点击获取更多步骤...
解题步骤 2.13.1
Perform the row operation to make the entry at a .
解题步骤 2.13.2
化简
解题步骤 2.14
Perform the row operation to make the entry at a .
点击获取更多步骤...
解题步骤 2.14.1
Perform the row operation to make the entry at a .
解题步骤 2.14.2
化简
解题步骤 2.15
Perform the row operation to make the entry at a .
点击获取更多步骤...
解题步骤 2.15.1
Perform the row operation to make the entry at a .
解题步骤 2.15.2
化简
解题步骤 2.16
Perform the row operation to make the entry at a .
点击获取更多步骤...
解题步骤 2.16.1
Perform the row operation to make the entry at a .
解题步骤 2.16.2
化简
解题步骤 2.17
Perform the row operation to make the entry at a .
点击获取更多步骤...
解题步骤 2.17.1
Perform the row operation to make the entry at a .
解题步骤 2.17.2
化简
解题步骤 2.18
Perform the row operation to make the entry at a .
点击获取更多步骤...
解题步骤 2.18.1
Perform the row operation to make the entry at a .
解题步骤 2.18.2
化简
解题步骤 3
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 4
The nullity is the number of columns without a pivot position in the row reduced matrix.