Prove or give a counterexample: If v1,…,vnv_1,\dots,v_nv1,…,vn and w1,…,wnw_1,\dots,w_nw1,…,wn are linearly independent lists of vectors in VVV, then v1+w1,…,vn+wnv_1+w_1,\dots,v_n+w_nv1+w1,…,vn+wn is linearly independent.
False, consider wk=−vkw_k = -v_kwk=−vk then the sum is all zeros.