Given the following vectors u and v, find a vector w in ³ so that {u,v,w} spans ³ and a non-zero vector z in ³ so that {u,v,z} does not span ³

my notes:

this is taken from lyryx textbook i have the correct answer at the back of book by i cannot reach it, please provide a walk through example of how to solve it.

u= [1]

[5]

[-4]

v = [-10]

[-2]

[-8]