Guys I am given a set of vectors $(v_1,\dots,v_{10}), \mathbb{R}^{10}, n=10$, which are linearly independent. It doesn't give me the values of the vectors but tells me to find if these are independent or not.
a. $v_1+v_2, v_2+v_3, v_3+v_4, v_4+v_1$
b. $v_1+v_2, 2(v_2+v_3), 3(v_3+v_4),..., 10(v_{10}+v_1)$
Not sure how to solve this. I know the definition of independency but I am having trouble applying it.