Para calcular a soma de duas transformações lineares, basta somar as transformações termo a termo. Dadas as transformações lineares: T(x,y,z) = (2x, x-y, y+z) S(x,y,z) = (x+2z, y, -z) Para calcular T + S, somamos cada componente das transformações: (T + S)(x,y,z) = T(x,y,z) + S(x,y,z) (T + S)(x,y,z) = (2x, x-y, y+z) + (x+2z, y, -z) (T + S)(x,y,z) = (2x + x + 2z, x-y + y, y+z - z) (T + S)(x,y,z) = (3x + 2z, x, y) Portanto, a alternativa correta é: b. (T+S)(x,y,z) = (3x+2z, x, y)

Vamos analisar cada opção: a. (T+S)(x,y,z)=(3x,−y,2z) T(x,y,z) = (2x, x-y, y+z) S(x,y,z) = (x+2z, y, -z) (T+S)(x,y,z) = T(x,y,z) + S(x,y,z) = (2x + x + 2z, x-y + y, y+z - z) = (3x+2z, x, y) b. (T+S)(x,y,z)=(3x+2z,x,y) T(x,y,z) = (2x, x-y, y+z) S(x,y,z) = (x+2z, y, -z) (T+S)(x,y,z) = T(x,y,z) + S(x,y,z) = (2x + x + 2z, x-y + y, y+z - z) = (3x+2z, x, y) c. (T+S)(x,y,z)=(2z,3x,y) T(x,y,z) = (2x, x-y, y+z) S(x,y,z) = (x+2z, y, -z) (T+S)(x,y,z) = T(x,y,z) + S(x,y,z) = (2x + x + 2z, x-y + y, y+z - z) = (3x+2z, x, y) d. (T+S)(x,y,z)=(3x+2z,y,z) T(x,y,z) = (2x, x-y, y+z) S(x,y,z) = (x+2z, y, -z) (T+S)(x,y,z) = T(x,y,z) + S(x,y,z) = (2x + x + 2z, x-y + y, y+z - z) = (3x+2z, x, y) e. (T+S)(x,y,z)=(3x,x,y) T(x,y,z) = (2x, x-y, y+z) S(x,y,z) = (x+2z, y, -z) (T+S)(x,y,z) = T(x,y,z) + S(x,y,z) = (2x + x + 2z, x-y + y, y+z - z) = (3x+2z, x, y) Portanto, a alternativa correta é a letra b. (T+S)(x,y,z)=(3x+2z,x,y).