(a) there exists a vector space consisting of exactly 100 vectors.
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Mathematics, 11.01.2020 02:31 Destiny8372
True or false and why?
(a) there exists a vector space consisting of exactly 100 vectors.
(b) there exists a vector space of dimension 100.
(c) in a vector space of dimension 3, any three vectors are linearly independent.
(d) in a vector space of dimension 3, any four vectors are linearly dependent.
(e) any vector space of dimension 2 has exactly two subspaces.
(f) any vector space of dimension 2 has in? nitely many subspaces.
(g) any vector space of dimension 3 can be expanded by four vectors.
(h) any vector space of dimension 3 can be expanded by two vectors.
(i) three vectors are linearly dependent if and only if one of them can be written as a linear combination of the other two.
(j) the column space and row space of the same matrix a will have the same dimension.
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True or false and why?
(a) there exists a vector space consisting of exactly 100 vectors.
(a) there exists a vector space consisting of exactly 100 vectors.
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