7. Let \( \mathbf{A} \) be an \( m\times n \) matrix. The linear system \( \mathbf{A}\mathbf{x} = \mathbf{b} \) has at most one solution for every \( \mathbf{b}\in \mathbb{R}^m \) if and only if the column vectors of \( \mathbf{A} \) are linearly independent.

阿摩線上測驗 · 2026-11-03T08:20:53+08:00

7. Let A be an m× n matrix. The linear system Ax = b has at most one solution for every b R^m if and only if the column vectors of A are linearly independent.

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7. Let \( \mathbf{A} \) be an \( m\times n \) matrix. The linear system \( \mathbf{A}\mathbf{x} = \mathbf{b} \) has at most one solution for every \( \mathbf{b}\in \mathbb{R}^m \) if and only if the column vectors of \( \mathbf{A} \) are linearly independent.

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