2. Show that the determinant map is continuous. det: Mat(n ×n, R) → R

Letf : R² → R be defined by ƒ((x, y)) = −3x – 7y. Is ƒ a linear transformation? a. f((x₁, y₁) + (x₂, y2)) = f((x₁, y₁)) + f((x₂, y2)) = Does f((x₁, y₁) + (x₂, y₂)) = f((x₁, y₁)) + f((x₂, y₂)) for all (x₁, y₁), (x₂, y₂) E R²? choose . (Enter x₁ as x1, etc.) 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

Compute the Jacobian of the mapping. G(r, t) = (2re", 3 + 8e")

Letf: R2. →R be defined by f((x, y)) = 4y - 3x. Is f a linear transformation? a. f((x₁, y₁) + (x2, y2)) = b. f(c(x, y)) = f((x₁, y₁)) + f((x2, y2)) = + Does f((x1, y1) + (x₂, y₂)) = f((x₁, y₁)) + f((x₂, y₂)) for all (x₁, y₁), (x2, y₂) E R²? choose (Enter x₁ as x1, etc.) c(f((x, y))) = Does f(c(x, y)) = c(f((x, y))) for all c ER and all (x, y) E R²? choose c. Is f a linear transformation? choose ⇒