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 a

{}\mathbb {R}

-basis of

{}\mathbb {R} ^{n}

.