作者JacobSyu (JacobSyu)
看板Grad-ProbAsk
標題[理工] 103台大-第3題 dimension
時間Sat Dec 27 01:30:38 2014
(a) If the dimension of the vector space M7x4(C) of matrices with senen rows
and four columns over the field C of complex numbers equals the dimension of
the vertor space R^n of n-tuples over the field R of real numbers, then
n=______.
(b) Let A be an mxn matrix over the field R of real numbers, if the m rows of
A are linearly independent, then the dimension of the vector space spanned by
the n rows of A is _____.
(c) If U and V are two distubct subspaces of a vector space W with dim(W)=6,
then dim(U∩V) is either _____ or _____.
(b):spanned by the n rows of A...考券應該打錯了columns
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推 mikeing27: (a)28 (b)m (c)看不懂不知道可以填啥 12/27 03:05
→ JacobSyu: 1nd soul, dim(U+V)=dim(U)+dim(V)-dim(U union V) 12/27 03:17
→ JacobSyu: subspace、sum space與原vector space維度相同(? 12/27 03:21
→ JacobSyu: 6=6+6-dim(U union V),dim(U union V)=6...? 觀念有誤 12/27 03:23
→ JacobSyu: 交集打成union... 12/27 03:35
→ JacobSyu: 謝謝mikeing27大,(a)(b)也在問,我真夠蠢= = 12/27 03:41
推 j897495: 第三題0～5都有可能資訊給太少了我覺得題目出錯或少給條 12/27 17:21
→ JacobSyu: 為什麼是0~5,子空間應該與原空間同維度才可比較吧 12/27 18:49
→ JacobSyu: 交集仍為子空間,聯集除非U包V or V包U 12/27 18:51
→ JacobSyu: 不要理我上上樓的回覆... 12/27 18:56