If B is a basis, then
for all scalars

,
and all vectors

,
in span (B).

Name: If B is a basis, then for all scalars , and all vectors , in span (B).
Brand: Quizplus
Rating: 4.8 (36 reviews)

Question

If B is a basis, then 
  for all scalars 
  
, 
  and all vectors 
  
, 
  in span (B).

Quizplus · Accepted Answer

This statement is true by the definition of a basis. A basis is a linearly independent set of vectors that span the entire vector space, which means that any vector in the span of the basis can be expressed as a linear combination of the basis vectors, and any scalar can be used to produce that combination.

If B Is a Basis, Then