Question

Qual é a transformação linear T : R^2 -> R^3 tal que T (1, 1) = (3, 2, 1) e T (0, −2) = (0, 1, 0)?

Answer 1

(x, y)= a(1,1)+b(0,-2)

(x, y) =(a, a) +(0,-2b)

(x, y) = (a, a-2b)

a=x

a-2b=y

x-2b=y

2b=x-y

b=(x-y)/2

(x, y)=x(1,1)+(x-y)/2(0,-2)

T(x, y) =xt(1,1)+(x-y)/2 t(0,-2)

T(x, y) =x(3,2,1)+(x-y)/2(0,1,0)

T(x, y) =(3x,2x,x) +(0,(x-y)/2,0)

$T(x, y) = (3x, \frac{5x - y}{2}, x)$