# Composition of linear transformations

1. Oct 25, 2011

### krozer

1. The problem statement, all variables and given/known data

Find two linear operators T and U on R^2 such that TU = 0 but UT ≠ 0.

3. The attempt at a solution

Let T(x1,x2)=(0,x2)

Let U(x1,x2)=(x2,0)

TU(x1,x2)=T(x2,0)=(0,0)

Am I right?

'Cause I can't remember if TU(x1,x2)=T[U(x1,x2)]

Or TU(x1,x2)=U[T(x1,x2)]

2. Oct 25, 2011

### micromass

Staff Emeritus
Looks good to me!!

And it's indeed

$$(TU)(x)=T(U(x))$$