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}

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), so .

And therefore the transformation is one-to-one? :) :) :)

Quote:

---

Originally Posted by divinelogos

And therefore the transformation is one-to-one? :) :) :)

---

Yes, for that reason is injective.