General Lin. Alg. Span Question

[hydralisks]

If a question asks "does v1, v2, v3 span R4"
can i just say no, regardless of what v1 v2 v3 is
because v1 v2 and v3 is just 3 dimensions while R4 needs 4 dimensions?

 

[fluidistic]

If a question asks "does v1, v2, v3 span R4"
can i just say no, regardless of what v1 v2 v3 is
because v1 v2 and v3 is just 3 dimensions while R4 needs 4 dimensions?

I'm almost sure you're right on this.

 

[hydralisks]

Thanks!

 

[HallsofIvy]

Yes. If a set of vectors spans a space, then some subset of it forms a basis for the space. Since no subset of 3 vectors can span a four dimensional set, this set cannot span R⁴.