# Finding the Kernel

• Dec 12th 2011, 05:33 PM
divinelogos
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!

http://img267.imageshack.us/img267/1910/capturehaw.jpg

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}
• Dec 12th 2011, 09:57 PM
FernandoRevilla
Re: Finding the Kernel
Quote:

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 $N(L)=\{\;\vec{0}_V\}$ .
• Dec 14th 2011, 03:17 PM
divinelogos
Re: Finding the Kernel
And therefore the transformation is one-to-one? :) :) :)
• Dec 14th 2011, 03:25 PM
FernandoRevilla
Re: Finding the Kernel
Quote:

Originally Posted by divinelogos
And therefore the transformation is one-to-one? :) :) :)

Yes, for that reason is injective.