Question

just #2

please show as much detail in steps , definitions, and what it means to be a one dim complex subspace

2. Find a one-dimensional complex subspace M CCsuch that R2 N M = {0}. 3. Let L:V → W be a linear map and N CW a subspace. Show that L-'(N) = {x V: L(x) E N}

Answer 1

2 The complen number set cis defined as c= xriyla, y ER} where th=-1, ne sai B={ 1, it is the basis fon the e. by definition of basis, it is liset Tv Span (B)= C. ce any neigtc we can empreess as a linean combination of B. n iy=nilting &mtily & C. C is recton space dim (6)=2. I onenir af cynol addition and in Sealan multiplication, Let m=& cx;o) Im er} (on mil toilmER? clearly mês a subset of C. 1 (0,0) Em (1) alt = 24 toi, ß= ng toi * ttp = 4thg toi 4 ev, CR Ч ч сік, ч, tg

& K+B EM li) het KER and Kantoi Em. ☆ Kd = kl M400) aku toi ; 2 кв м. (2 км ek). From ù, l'i) and (iii) , we conclude that by definition of Subspace Mis a subspace of cho clearely 1R2 = { (m, 3) lm, st R} and m= (,0) | mer] .: ROm =$10,017-30). Zero reeton.