Home/Algebra/Vectors/Linear combination15. VectorsLinear combinationLevel: intermedioIn 15. VectorsFormulaCopy LaTeXw=c1v1+⋯+ckvkw=c_1v_1+\cdots+c_kv_kw=c1v1+⋯+ckvkTagsalgebraalgebra formulalinearvectorsvectors algebraDetailBuilds new vectors from a given set.Explore the ideaFound an error? Contact us.Related formulasRelatedSpanspan(v1,…,vk)={∑icivi}\operatorname{span}(v_1,\ldots,v_k)=\{\sum_i c_iv_i\}span(v1,…,vk)={i∑civi}Open formulaOpen in sectionRelatedLinear independence∑icivi=0⇒c1=⋯=ck=0\sum_i c_iv_i=0\Rightarrow c_1=\cdots=c_k=0i∑civi=0⇒c1=⋯=ck=0Open formulaOpen in section