Question

When are vectors in $\mathbb{R}^n$ equivalent?

Answer 1

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 $\mathbf{v}=\mathbf{w}$.