試題詳解

13. (5%) Let vi, ... , Vn be vectors in a vector space V for n ＞ 0.Which statement is NO'T correct?
(A) If the dimension of V is n, and vi, ... , In span V, then yi, ... , vn are linearly independent
(B) If the dimension of V is m, and m ＞ n, then vi, ... , vn can be extended to form a basis for V
(C) If the dimension of V is m, and m ＜ n, then vi, ... , In are linearly dependent
(D) If both fu, ... , Ms and fu, ... , um； are bases for a vector space V, then n = m
(E) A vector v in Span(vI, v) can be written uniquely as a linear combination of VI, ... , In if and only if v, , vn are linearly independent [4 7 37