Please note: This question does not count for my grade. It comes from a final study guide. Can someone please verify I did it (part d) correctly? Thanks!

Attempt at Solution:

(a1+1)+(a2+2)t=0

This gives the system:

a1+1=0

a2+2=0

So,

a1=-1

a2=-2

So the set of all vectors for which L(a1,a2)=0 is:

N(L)={(a1,a2)|a1=-1 and a2=-2}