Let f : R → R be defined by f(x) = 9x. Is f a linear transformation? a. f(x + y) = f(x) + f(y) = Does f(x + y) = f(x) + f(y) for all æ, y E R? choose b. f(cx) c(f(x)) Does f(cæ) = c(f(x)) for all c, x € R? choose c. Is f a linear transformation? choose >

Letf : R² → R be defined by f((x, y)) = −7x − 9y. Is ƒ a linear transformation? a. f((x₁, y₁) + (x2, Y₂)) = as x1, etc.) f((x₁, y₁)) + f((x2, 3/2)) = Does f((x₁, y₁) + (x2, Y2 )) = f((x₁, y₁ )) + ƒ((x2, y2)) for all (x₁, y₁), (x2, y₂) € R²? choose + b. f(c(x, y)) = c(f((x, y))) = = Does f(c(x, y)) = c(f((x, y))) for all c E R and all (x, y) = R²? choose c. Isf a linear transformation? choose . (Enter X₁

Let f: R → R³ be defined by f(x) a. f(x + y) b. f(cx) = = f(x) + f(y) = + Does f(x + y) = f(x) + f(y) for all x, y ER? choose = = (7x, 7x, 2x). Is f a linear transformation? c(f(x)) Does f(cx) = c(f(x)) for all c, x € R? choose c. Is f a linear transformation? choose