For u, v € R³, which of the following is (are) inner

Last updated: 8/11/2022

For u, v € R³, which of the following is (are) inner product(s)? (A) (u, v) = U₁V₁ + ZU₂V₂ + 5u3V3 (B) (u, v) = U₁V₁ - U₂V₂ + ZU3V3 (C) (u, v) = u²v₁ + U₂V² + U3V3 (D) (u, v) = U₁V₂ + U2V3 + U3V1 (E) (u, v) = U₁U₂Uz + V₁ V₂ V3 Which of the following is (are) linear transformation(s)? (A) f(x) = sin x + cos x (B) f(x) = ex(x² + x). (C) T(x, y) = (x + y, x - y). (D) T(x, y, z) = (x − 2y, 0, x + 3y - z). (E) T(x, y) = (x − 1, y + 1, x + z)