线性代数 示例

求出零空间 s={[[2],[-1],[3],[4],[2]],[[6],[2],[-1],[3],[4]]}
解题步骤 1
Write as an augmented matrix for .
解题步骤 2
求行简化阶梯形矩阵。
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解题步骤 2.1
Multiply each element of by to make the entry at a .
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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 .
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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 .
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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 .
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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 .
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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 .
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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 .
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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 .
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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 .
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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
Perform the row operation to make the entry at a .
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解题步骤 2.10.1
Perform the row operation to make the entry at a .
解题步骤 2.10.2
化简
解题步骤 3
Use the result matrix to declare the final solution to the system of equations.
解题步骤 4
Write a solution vector by solving in terms of the free variables in each row.
解题步骤 5
Write as a solution set.