It is like a class discussion and we're supposed to write a discussion about Vector spaces,...

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Advance Math

It is like a class discussion and we're supposed to write adiscussion about Vector spaces, subspaces and bases
Overview (what to write on the discussion): So we'resupposed to discuss and explain about these followingpoints:
Vector Spaces, Definitions, Examples, Non Examples
Spanning Sets, Linear Independence
Basis, Dimension
Rank
Change of Basis, Coordinates
PUT EXAMPLES AND DEFINITIONS (EX: Showing examples tovector addition (closure under addition, etc) and scalarmultiplication (distributive property, etc)
Instructions:
Add a new discussion topic. In your post, please include thefollowing:
Details on proofs.
Illustrate examples of special interest.
Apply your mathematical knowledge of given structures inproving or disproving assertions regarding Vector Spaces.

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4.2 Ratings (619 Votes)

Definition of Spanning Set of a Vector SpaceLet Sv1v2vnSv1v2vn be a subset of a vector spaceVV The set is called a spanning set of VV if every vectorin VV can be written as a linear combination of vectors in SS Insuch cases it is said that SS spans VVDefinition of the span of a set IfSv1v2vnSv1v2vn is a set of vectors in a vectorspace VV then the span of SS is See Answer

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