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## Main Question or Discussion Point

I'm having trouble conceptualizing exactly what a subspace is and how to identify subspaces from vector spaces.

I know that the definition of a subspace is:

A subset W of a vector space V over a field [itex]\textbf{F}[/itex] is a subspace if W is also a vector space over [itex]\textbf{F}[/itex] w/ the operations of vector addition and scalar multiplication.

So if I have to define a subspace of [itex]\textbf{R^3}[/itex], is it enough to show that the new vector, say W, exists in [itex]\textbf{R^3}[/itex]?

I know that the definition of a subspace is:

A subset W of a vector space V over a field [itex]\textbf{F}[/itex] is a subspace if W is also a vector space over [itex]\textbf{F}[/itex] w/ the operations of vector addition and scalar multiplication.

So if I have to define a subspace of [itex]\textbf{R^3}[/itex], is it enough to show that the new vector, say W, exists in [itex]\textbf{R^3}[/itex]?