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6 Nov 2019
State "True" or "False" for each of the following statements. You do not need to justify your answers. There exists a vector space consisting of exactly 100 vectors. There exists a vector space of dimension 100. In a vector space of dimension 3, any three vectors are linearly independent. In a vector space of dimension 3, any four vectors are linearly dependent. Any vector space of dimension 2 has exactly two subspaces. Any vector space of dimension 2 has infinitely many subspaces. Any vector space of dimension 3 can be expanded by four vectors. Any vector space of dimension 3 can be expanded by two vectors. Three vectors are linearly dependent if and only if one of them can be written as a linear combination of the other two. The column space and row space of the same matrix A will have the same dimension. Show transcribed image text
State "True" or "False" for each of the following statements. You do not need to justify your answers. There exists a vector space consisting of exactly 100 vectors. There exists a vector space of dimension 100. In a vector space of dimension 3, any three vectors are linearly independent. In a vector space of dimension 3, any four vectors are linearly dependent. Any vector space of dimension 2 has exactly two subspaces. Any vector space of dimension 2 has infinitely many subspaces. Any vector space of dimension 3 can be expanded by four vectors. Any vector space of dimension 3 can be expanded by two vectors. Three vectors are linearly dependent if and only if one of them can be written as a linear combination of the other two. The column space and row space of the same matrix A will have the same dimension.
Show transcribed image text Keith LeannonLv2
6 Nov 2019
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