問題詳情

15. (5%) Which of the following statements are correct?
(A) A basis for a subspace is a linearly independent subset of the subspace that is as large aspossible.
(B) If V is a subspace of dimension k, then every generating set for V contains exactly kvectors.
(C)

is any basis for Rn, then there exists a vector v

so that vcan not be expressed as a linear combination of bi, ba...., bn.
(D) Let T be a linear operator on Rn, and u and V be two bases forRn. Denote [T]Bas therepresentative matrix of T with respect to any basis B for Rn. Then, [T]u and [T]v aresimilar.
(E) If B is a basis for Rn and T is the identity operator on R", then [T]B = In.

參考答案

答案：[無官方正解]
難度：計算中-1
書單：沒有書單，新增