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.