线性代数 示例

解题步骤 1
Find the determinant.
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解题步骤 1.1
Choose the row or column with the most elements. If there are no elements choose any row or column. Multiply every element in column by its cofactor and add.
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解题步骤 1.1.1
Consider the corresponding sign chart.
解题步骤 1.1.2
The cofactor is the minor with the sign changed if the indices match a position on the sign chart.
解题步骤 1.1.3
The minor for is the determinant with row and column deleted.
解题步骤 1.1.4
Multiply element by its cofactor.
解题步骤 1.1.5
The minor for is the determinant with row and column deleted.
解题步骤 1.1.6
Multiply element by its cofactor.
解题步骤 1.1.7
The minor for is the determinant with row and column deleted.
解题步骤 1.1.8
Multiply element by its cofactor.
解题步骤 1.1.9
Add the terms together.
解题步骤 1.2
乘以
解题步骤 1.3
计算
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解题步骤 1.3.1
可以使用公式 矩阵的行列式。
解题步骤 1.3.2
化简行列式。
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解题步骤 1.3.2.1
化简每一项。
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解题步骤 1.3.2.1.1
乘以
解题步骤 1.3.2.1.2
乘以
解题步骤 1.3.2.2
中减去
解题步骤 1.4
计算
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解题步骤 1.4.1
可以使用公式 矩阵的行列式。
解题步骤 1.4.2
化简行列式。
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解题步骤 1.4.2.1
化简每一项。
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解题步骤 1.4.2.1.1
乘以
解题步骤 1.4.2.1.2
乘以
解题步骤 1.4.2.2
中减去
解题步骤 1.5
化简行列式。
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解题步骤 1.5.1
化简每一项。
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解题步骤 1.5.1.1
乘以
解题步骤 1.5.1.2
乘以
解题步骤 1.5.2
相加。
解题步骤 1.5.3
相加。
解题步骤 2
Since the determinant is non-zero, the inverse exists.
解题步骤 3
Set up a matrix where the left half is the original matrix and the right half is its identity matrix.
解题步骤 4
求行简化阶梯形矩阵。
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解题步骤 4.1
Multiply each element of by to make the entry at a .
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解题步骤 4.1.1
Multiply each element of by to make the entry at a .
解题步骤 4.1.2
化简
解题步骤 4.2
Perform the row operation to make the entry at a .
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解题步骤 4.2.1
Perform the row operation to make the entry at a .
解题步骤 4.2.2
化简
解题步骤 4.3
Perform the row operation to make the entry at a .
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解题步骤 4.3.1
Perform the row operation to make the entry at a .
解题步骤 4.3.2
化简
解题步骤 4.4
Multiply each element of by to make the entry at a .
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解题步骤 4.4.1
Multiply each element of by to make the entry at a .
解题步骤 4.4.2
化简
解题步骤 4.5
Perform the row operation to make the entry at a .
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解题步骤 4.5.1
Perform the row operation to make the entry at a .
解题步骤 4.5.2
化简
解题步骤 4.6
Multiply each element of by to make the entry at a .
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解题步骤 4.6.1
Multiply each element of by to make the entry at a .
解题步骤 4.6.2
化简
解题步骤 4.7
Perform the row operation to make the entry at a .
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解题步骤 4.7.1
Perform the row operation to make the entry at a .
解题步骤 4.7.2
化简
解题步骤 4.8
Perform the row operation to make the entry at a .
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解题步骤 4.8.1
Perform the row operation to make the entry at a .
解题步骤 4.8.2
化简
解题步骤 4.9
Perform the row operation to make the entry at a .
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解题步骤 4.9.1
Perform the row operation to make the entry at a .
解题步骤 4.9.2
化简
解题步骤 5
The right half of the reduced row echelon form is the inverse.
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