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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.
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