Field extension/Q in R/Basis/Exercise

Let ${}\mathbb {Q} ^{n}$ be the ${}n$-dimensional standard vector space over ${}\mathbb {Q}$, and let ${}v_{1},\ldots ,v_{n}\in \mathbb {Q} ^{n}$ be a family of vectors. Prove that this family is a ${}\mathbb {Q}$-basis of ${}\mathbb {Q} ^{n}$ if and only if the same family, considered as a family in ${}\mathbb {R} ^{n}$, is an ${}\mathbb {R}$-basis of ${}\mathbb {R} ^{n}$.

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