Composition of linear transformations

[krozer]

Homework Statement

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

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)]

 

[micromass]

Looks good to me!

And it's indeed

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