試題詳解

22.Let A ∈ , denote the column space of A, denote the null space of A,
and dim(S) denote the dimension of a subspace S. Which of the following statements are true?
(A) For any x ∈ , there exists u ∈ and v ∈ such that x = u + v.
(B) Suppose u ∈ and v ∈ . Then = 0.
(C) dim+ dim =n
(D) For any y ∈ , there exists x ∈ such that y = .

(E) Ify ∈ , then y is the zero vector in .