If s and t are linear transformation then what is st
Answers
Answered by
0
A finite dimensional vectors space VV, and two linear transformations on VV, SS and TT.
I need to show that N(ST)≤N(S)+N(T)N(ST)≤N(S)+N(T). Can anybody spot what is wrong with this argument:
N(ST)=dim(ker(ST))N(ST)=dim(ker(ST)) now call S1S1 the restriction of SS to Im TIm T, so ker(S1)=ker(S)ker(S1)=ker(S)intersect Im (T)Im (T) so then N(S1)<N(S)N(S1)<N(S) hence N(ST)<N(S)N(ST)<N(S)?
I need to show that N(ST)≤N(S)+N(T)N(ST)≤N(S)+N(T). Can anybody spot what is wrong with this argument:
N(ST)=dim(ker(ST))N(ST)=dim(ker(ST)) now call S1S1 the restriction of SS to Im TIm T, so ker(S1)=ker(S)ker(S1)=ker(S)intersect Im (T)Im (T) so then N(S1)<N(S)N(S1)<N(S) hence N(ST)<N(S)N(ST)<N(S)?
Similar questions