State \"True\" or \"False\" for each of the following statements. You do not nee

Question

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.

Explanation / Answer

b) there exists a vector space of dimension 100 ---- statement is true

i) three vectors are linearly dependent if and only if one of them can be written as linear combination of other two ---- statement is true

j) row space and column space of a matrix have same dimension --- true

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