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Let \(A: \mathbb{R}^{n} \rightarrow \mathbb{R}^{k}\) be a real matrix, not necessarily square.

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Let \(A: \mathbb{R}^{n} \rightarrow \mathbb{R}^{k}\) be a real matrix, not necessarily square.

a) If two columns of \(A\) are the same, show that \(A\) is not one-to-one by finding a vector \(x=\left(x_{1}, \ldots, x_{n}\right)\) that is in the nullspace of \(A\).
b) More generally, if the columns of \(A\) are linearly dependent, show that \(A\) is not one-to-one.
in Mathematics by ♦ Platinum (164,236 points) | 194 views

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