Originally Posted by

**manygrams** 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 $\displaystyle \rightarrow$ 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 $\displaystyle \in$ V X V | Ta=0}

0 =Ta

=T(x,y)

= x-y

y = x

Therefore, Ker T = {(x,y)$\displaystyle \in$ V X V | x=y}

Im T = T(V X V) = {Ta | a $\displaystyle \in$ V}

= T(x,y)

= x - y $\displaystyle \forall x,y \in V$

Make sense?