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When are vectors in $\mathbb{R}^n$ equivalent?
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Vectors $\mathbf{v}=\left(v_{1}, v_{2}, \ldots, v_{n}\right)$ and $\mathbf{w}=\left(w_{1}, w_{2}, \ldots, w_{n}\right)$ in $R^{n}$ are said to be equivalent (also called equal) if $$v_{1}=w_{1}, \quad v_{2}=w_{2}, \ldots, \quad v_{n}=w_{n}$$ We indicate this by writing $\mathbf{v}=\mathbf{w}$.
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