shif

Did you watch any of them? Can you recommend a one you specially liked?

I also think that linear vector space and vector space are the same thing (at least in the usual terminology).

u1, u2 and u3 are the basis of the linear space they span (they are lin. indep. and span it by def.) Write v1, v2 and v3 in a matrix according to the basis {u1,u2,u3} and you get 1 1 1 1 a 0 0 1 b the will be lin. dep. if and only if we can make a zero row with Gauss elimination which is if and only if b(a-1)+1=0 (if I am not mistaken)