Defining a statement (Vector Algebra)

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Homework Help Overview

The discussion revolves around the definition of the term "span" in the context of vector spaces, specifically regarding a set of vectors belonging to a vector space V over a field F.

Discussion Character

  • Conceptual clarification

Approaches and Questions Raised

  • Participants explore the implications of the statement that a set of vectors spans a vector space, questioning whether this indicates linear dependence or independence.

Discussion Status

Some participants are seeking clarification on the definition of "span," while others emphasize the need for additional information about the vector space to determine the nature of the vectors involved. The original poster's attempt to define the concept has prompted further inquiry into the meaning of spanning sets.

Contextual Notes

There is an indication that the problem may be constrained by the definitions provided in a textbook, which could influence the understanding of the term "span."

JFonseka
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Homework Statement



Let V be a vector space over the field F. Define what is meant by the statement
"For vectors v1, v2,...,vn belonging to V, the set {v1,v2,...,vn} spans V

Homework Equations



None

The Attempt at a Solution



Does it mean that the set is linearly dependent?
 
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You can't tell whether the vectors are linearly dependent or linearly independent without knowing more about your vector space V.

Doesn't your book have a definition of the term "span"?
 
So it is a spanning set for V?
 
The problem tells you that this set spans V. You are supposed to say what this means.
 

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