Let {~u, ~v, ~w} be a basis for a vector space V . Show that {~u...

Since Space Now {ru, no, ww} is a basis for a vector V. , then. {rel., ,,~W} is linearly independent and dim (v)= 3. cosider the relation , (aut no) + C₂ (~W) + Cg (~ UtwW) = 0 , where a. (2) - (C, +C) (ace) +(cit la Xaro ) + (3 (~W) = 0 =) (C1+19)=0, Cit(2=0 (3 belongs, to the the field. of the vector space is a .: w utro linearly nutre, ~, and Cz = 0 [since &au, wo, wwf is linearly indepondant -) G=0, (:0, 13.20 urn W} independent set. Visa vector space of dimension 3 and {~utno, no, nutaw} is a ww} is a linearly independent set containing 3 vectors of v. ,NWA ww} is a basis for v. v Nu of NV )