A basis for a vector space must consist of linearly independent vectors that span the entire space. In the case of R4, a minimum of four linearly independent vectors is required to form a basis. The discussion highlights a common misconception where two vectors are mistakenly thought to span R4, which is impossible unless referring to a subspace of R4. Therefore, any claim of two vectors forming a basis for R4 is incorrect.
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A set of two basis vectors couldn't possibly span R4. Are you sure that what you saw wasn't talking about a subspace of R4?grassstrip1 said:Hey everyone I just had a quick thought that was bothering me. For a set to be a basis it must be linearly independent and span the vector space. I've seen cases however of only two vectors forming a basis for R4 I don't see how two vectors could span 4 space or am I missing something.
Thanks!