线性代数 示例

求出零空间 [[0,10,20,30],[25,45,65,85]]
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
Swap with to put a nonzero entry at .
解题步骤 2.2
Multiply each element of by to make the entry at a .
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解题步骤 2.2.1
Multiply each element of by to make the entry at a .
解题步骤 2.2.2
化简
解题步骤 2.3
Multiply each element of by to make the entry at a .
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解题步骤 2.3.1
Multiply each element of by 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 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 the solution as a linear combination of vectors.
解题步骤 6
Write as a solution set.