[Transformação Linear] Nucleo e Imagem, ache a transformaçao

por **vualas** » Qua Nov 07, 2012 00:37

ACHE A TRANSFORMAÇÃO LINEAR:
T:R4->R4 tal que
Nuc(T): [(1,0,1,0),(-1,0,0,1)
Im(T): [(1,-1,0,2),(0,1,-1,0)]

como fazer??

por **adauto martins** » Qui Dez 15, 2016 08:00

temos que:
T(1,0,1,0)=T(-1,0,0,1)=(0,0,0,0)

,pois $(1,0,1,0),(-1,0,0,1)\in NUC(T)...$
e $T({u}_{1})=(1,-1,0,2),T({u}_{2})=(0,1,-1,0)$ ,p/ ${u}_{1},{u}_{2} $\not\in$ NUC(T)$ ...logo podemos ter
p/ algum $v \in IM(T):T(x,y,z,w)=x.T({u}_{1})+y.T({u}_{2})+z.(1,0,1,0)+w.(-1,0,0,1)=x.(1,-1,0,2)+y.(0,1,-1,0)+z(0,0,0,)+w.(0,0,0,0)$ $\Rightarrow T(x,y,z,w)=(x,-x,0,2x)+(0,y,-y,0)=(x,-(x+y),-y,2x)...$