Question

Álgebra Linear


Determinar a transformação Linear T:R³⇒R³ tal que T(1,-1,0)=(1,1), T(0,1,1)=(2,2) e T(0,0,1)=(3,3).

Answer 1

Resposta:

T:R³⇒R² tal que T(1,-1,0)=(1,1), T(0,1,1)=(2,2) e T(0,0,1)=(3,3)

(x,y,z)=a(1,-1,0)+b(0,1,1)+c(0,0,1)

x=a  ==>a=x

y=-a+b   ==>b=y+x

z=b+c  ==>c=z-b ==>c=z-(y+x) =z-y-x

(x,y,z)=x*(1,-1,0)+(x+y)*(0,1,1)+(z-y-x)*(0,0,1)

T(x,y,z)=x*T(1,-1,0)+(x+y)*T(0,1,1)+(z-y-x)*T(0,0,1)

T(x,y,z)=x*(1,1)+(x+y)*(2,2))+(z-y-x)*(3,3)

T(x,y,z)=(x+2x+2y+3z-3y-3x ; x+2x+2y+3z-3x-3y)

T(x,y,z)=(3z-y ; 3z-y)