Question

It is given that the vectors v1=[ 1 0]^T and v2 = [ 0 1]^T span the full two-dimensional space R^2(R - set of real numbers)

Also it is given that the vectors v1=[1 0]^T , v2 = [0 1]^T and v3 = [4 7]^T , span the full space R^2.

Could you please clarify the difference between ful two-dimensional space R^2 and full space R^2?

Thank you!

Answer 1

since v1 and v2 span R^2, any linear combination of them can be added, and the new set of vectors will also span r^2. It's just not a minimal spanning set.

Ya got me on the difference between 2D space and full space. Guess you'll have to go to google after all.