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Let $\left\{e_{1}, e_{2}, \ldots, e_{n}\right\}$ be the standard basis in $\mathbb{R}^{n}$ and let $\left\{v_{1}, v_{2}, \ldots, v_{n}\right\}$ be another basis in $\mathbb{R}^{n}$. Find a matrix $A$ that maps the standard basis to this other basis.
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