Chapter 3.3, Problem 6E

Let ${\text{x}}_1,{\text{x}}_2$ , and ${\text{x}}_3$ be linearly independent vectors in ${ℝ}^n$ and let
${\text{y}}_1={\text{x}}_1{\text{+x}}_2,{\text{y}}_2={\text{x}}_2{\text{+x}}_3,{\text{y}}_3={\text{x}}_3{\text{+x}}_1$
Are ${\text{y}}_1,{\text{y}}_2$ , and ${\text{y}}_3$ linearly independent? Prove your answer.