I can answer question 2 the reason is any set of 6 vectors in R5 is linearly dependent, even though some sets of 6 vectors in R5 span R5. To be a basis it must be a linearly independent spanning set, so if it's linearly dependent, it cannot be a basis.
But actually I know the answer for all of...
Homework Statement
Definition of spanning set:
Let be vectors in the vector space . The set of all linear combination of the vectors is a subspace ( say ) of . The subspace is called the space spanned by the vectors The set is called a spanning set of .
Definition of linear independence...