1.9.7 Linear spaces

Problem: Prove that the set of \( n \)-dimensional vectors \( L=\{\bar{a}=\underbrace{(\alpha, \beta, \alpha, \beta, \ldots)}_{n} \mid \alpha, \beta \in R\} \quad \) is the subspace of the space \( \mathbb{R}^{n} \), find the basis and dimension of this subspace.