Question

what is the dimension of a vector space ''v'' if v{0}?

Answer 1

if V just consists of the zero vector, the dimension is 0.

Answer 2

how the dimension is zero please explain if u can??

Answer 3

Its by definition, so the Fundamental Theorem of Linear Algebra holds. If you have a Linear Transformation from one space to another:\[T:\mathbb{R}^m\longrightarrow \mathbb{R}^n\], then one part of the FToLA has to do with the dimension of the Null Space of T and the Row Space of T adding up to "m", the dimension of the domain of the transformation. If a vector space that only contains the zero vector had a dimension other than zero, this theorem wouldnt hold. Have you seen this theorem before?

Answer 4

no. can u explain my que in another but easy way?

Answer 5

Its really just by definition, something you just accept. If you want a proof, its what i posted above =/ There isnt an easy way to explain it concretely.

I mean, I can say stuff like, "Its the zero vector, it doesnt have any length, its just a point, so it doesnt have dimension", but thats just waving my hands around, nothing something I consider a proof.