Question Number 100311 by mathocean1 last updated on 26/Jun/20

Answered by mathmax by abdo last updated on 26/Jun/20

M(f,B) = (((1      2)),((1       0)) )  ⇒f(i) =i+j and f(j) =2i  g =f+id_E    and h =f−2id_E  ⇒g(u) =f(u)+u  and h(u)=f(u)−2u ⇒  g(i) =f(i)+i =2i+j  and  g(j) =f(j)+j =2i+j ⇒  M(g,B) = (((2          2)),((1           1)) )  h(i) =f(i)−2i =i+j−2i =−i+j  h(j) =f(j)−2j =2i−2j ⇒M(h,B) = (((−1      2)),((1         −2)) )  2) ker g ={u /g (u) =0}  g(u)=0 ⇒M_g .u =0 ⇒ (((2          2)),((1          1)) ) ((x),(y) )=0 ⇒ { ((2x+2y=0)),((x+y =0)) :}  ⇒y =−x ⇒(x,y) =x(1,−1) =xe_1  with e_1 (1,−)  ker g is a line  3) kerh ={u/h(u)=0}  h(u)=0 ⇒M_h .u =0 ⇒ (((−1           2)),((1                −2)) ) ((x),(y) )=0⇒ { ((−x+2y =0)),((x−2y =0)) :}  ⇒x =2y ⇒(x,y) =(2y,y) =y(2,1) =ye_2  with e_2 (2,1)

Commented bymathocean1 last updated on 26/Jun/20

Thank you very much sir!  It is too great... May  God bless you

Commented bymathmax by abdo last updated on 26/Jun/20

you are welcome.