Hi there,
I was just wondering if anyone could tell me if my answer was somewhat right.
An example in my textbook asks:
If T:V X V V is the linear mapping T(x,y)=x-y, determine the kernel and range of T.
My Answer:
Let a=(x,y)
Ker T = {a V X V | Ta=0}
0 =Ta
=T(x,y)
= x-y
y = x
Therefore, Ker T = {(x,y) V X V | x=y}
Im T = T(V X V) = {Ta | a V}
= T(x,y)
= x - y
Make sense?