Question

Determine whether or not the given vectors in R^n form a basis for R^n:
v1=(0,7,-3)
v2=(0,5,4)
v3=(0,5,10)

Answer 1

No they don't. I assume you meant that this "n" number of vectors is supposed to form a basis for R^n. n=3 and these vectors do not span R^3 because you can't define any vector in R^3 using these vectors. Any vector of the form <n 0 0> (where n is any number) could not be written as a sum of these 3 given vectors.

Answer 2

because none of these vectors has a component in the "x-direction" or "i direction" (when using a standard xyz or ijk coordinate system.

Answer 3

Thanks a lot. I've been having a lot of trouble with this unit on vector spaces. Linear algebra is really a tough subject in my opinion.

Answer 4

yeah it is kind of abstract sometimes