8. Is there a linear transformation T' : Rº → Rª such that T(1,0, 3) = (1, 1) and T(-2, 0, -6) = (2, 1) ? Explain.

Show that the following are not llinear transformations, explain why. T(x,y) = (x^3, xy, y) T(x,y) = (x-2, y+2)

2. Let T : R² → R² be a linear transformation such that: 1 -2 (i) T maps vector u = into the vector a = [ 5 3 (ii) T maps vector v = [³] into the vector b = [ Use the fact that T is a linear transformation to find T(3u +2v). -4

Let f: R² → R be defined by f((x, y)) = -8-8y +6. Is ƒ a linear transformation? a f((₁, ₁) + (12, Y2)) = f((₁, 1)) + f((F2, Y2)) = Does f((11, y1) + (12, Y2)) = f((F1, Y₁)) + f((2, 2)) for all (T₁, Y₁), (2, Y2) € R²? choose b. f(c(x, y)) = c(f((x, y))) = Does f(c(x, y)) = c(f((x, y))) for all c R and all (x, y) = R²? choose c. Is f a linear transformation? choose (Enter ₁ as x1, etc.)