1. ## Finding the Kernel

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}

2. ## Re: Finding the Kernel

Originally Posted by divinelogos
So the set of all vectors for which L(a1,a2)=0 is:
N(L)={(a1,a2)|a1=-1 and a2=-2}
Right, and from (a), $\vec{0}_V=(-1,-2)$ so $N(L)=\{\;\vec{0}_V\}$ .

3. ## Re: Finding the Kernel

And therefore the transformation is one-to-one?

4. ## Re: Finding the Kernel

Originally Posted by divinelogos
And therefore the transformation is one-to-one?
Yes, for that reason is injective.