Transformações e Espaços Lineares

[bebelo32]

1) Ache a transformação linear T R³? R²
tal que t (1,0,0) = (2,0),T(0,1,0) = (1,1) e T(0,0,1) = (0,-1)

R : [ 1,0,0) , (0,1,0) ,(0,0,1) ] base R³
seja (x,y,z) ? R³


T(1,0,0) = (2,0)
T(0,1,0) = (1,1)
T(0,0,1) = (0,-1)
(x,y,z) = a(1,0,0) + b (0,1,0) + c (0,0,1)
(x,y,z) = (a,0,0) +(0,b,0) + (0,0,c) = (x,y,z) (a,b,c)
x=a
y=b
z=c
(x,y,z) = x(1,0,0) + y(0,1,0) +z(0,0,1)
T(x,y,z) = xT(1,0,0)+yT(0,1,0)+zT(0,0,1)
T(x,y,z) = x(2,0)+y(1,1) +z(0,-1)
T(x,y,z) = (2x,0)+(y,y) +(0,-z)
T(x,y,z) = (2x+y,y-z)

essa questao esta certa