試題詳解

38. Which of the following statements is true?
(A) Let A be an arbitrary matrix of size m X n. If m ＞ n, then rank( A ) ＜ rank(A^t).
(B) Let A be an arbitrary matrix of size m ✖n. If m ＞ n,then rank( A ) ＞ rank(A^t).
(C) If W₁, W₂ are two subspaces of V, then the union W₁U W₂ is also a subspace of V.
(D) Let W be a subspace of a vector space V. Then, dim(W) ≤ dim(V).
(E) Let A be a square matrix, k be a constant. Then, det(kA) = kdet( A ).