Given are $n$-dimensional vector space $\langle R^n;+\mid R\rangle$ and $n$ vectors $(v_1,v_2,\ldots,v_n)$ which are linearly independent, $u_i\in R^n, i=\overline{1,n}.$
Say, $x$ = $(v_1,v_2,\ldots,v_n)$ and $y$ = $(u_1,u_2,\ldots,u_n)$. Then $x+y\in R^n$. Vectors are both $n$-dimensional.
Q: So, by that way, are the $n$ vectors in $x+y$ linearly independent? Is there some theorem which relates to this?