Math  /  Algebra

QuestionFind a basis for the column space of A=[420144314201]A=\left[\begin{array}{cccc} 4 & 2 & 0 & -1 \\ -4 & -4 & -3 & 1 \\ 4 & 2 & 0 & -1 \end{array}\right]

Studdy Solution
提取主列对应的原始列向量作为列空间的基。
从原始矩阵 A A 中提取第一列和第二列: [444],[242]\begin{bmatrix} 4 \\ -4 \\ 4 \end{bmatrix}, \begin{bmatrix} 2 \\ -4 \\ 2 \end{bmatrix}
因此,列空间的基为: {[444],[242]}\left\{ \begin{bmatrix} 4 \\ -4 \\ 4 \end{bmatrix}, \begin{bmatrix} 2 \\ -4 \\ 2 \end{bmatrix} \right\}

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