Linear Algebra, spanned by vectors

[rocomath]

How is this "All of R^3"

Describe the subspace of R^3 spanned by: all vectors with positive components.

Answer is, All of R^3. I don't get how it's all of R^3 though because if the components are all positive, it's only spanning in the positive direction? What about the negative portion? That is excluded, so it's not all of R^3.

 

[Defennder]

That may be so, but the linear coefficients of the positive vectors may be negative.

 

[rocomath]

That may be so, but the linear coefficients of the positive vectors may be negative.

Ah, I c! Thanks.