线性代数 示例

判断是否为线性相依 s={[[6],[2],[1]],[[4],[-3],[1]]}
解题步骤 1
To determine if the columns in the matrix are linearly dependent, determine if the equation has any non-trivial solutions.
解题步骤 2
Write as an augmented matrix for .
解题步骤 3
求行简化阶梯形矩阵。
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解题步骤 3.1
Multiply each element of by to make the entry at a .
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解题步骤 3.1.1
Multiply each element of by to make the entry at a .
解题步骤 3.1.2
化简
解题步骤 3.2
Perform the row operation to make the entry at a .
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解题步骤 3.2.1
Perform the row operation to make the entry at a .
解题步骤 3.2.2
化简
解题步骤 3.3
Perform the row operation to make the entry at a .
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解题步骤 3.3.1
Perform the row operation to make the entry at a .
解题步骤 3.3.2
化简
解题步骤 3.4
Multiply each element of by to make the entry at a .
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解题步骤 3.4.1
Multiply each element of by to make the entry at a .
解题步骤 3.4.2
化简
解题步骤 3.5
Perform the row operation to make the entry at a .
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解题步骤 3.5.1
Perform the row operation to make the entry at a .
解题步骤 3.5.2
化简
解题步骤 3.6
Perform the row operation to make the entry at a .
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解题步骤 3.6.1
Perform the row operation to make the entry at a .
解题步骤 3.6.2
化简
解题步骤 4
Remove rows that are all zeros.
解题步骤 5
Write the matrix as a system of linear equations.
解题步骤 6
Since the only solution to is the trivial solution, the vectors are linearly independent.
线性无关