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Composition of linear transformations

  • Thread starter krozer
  • Start date
  • #1
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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)]
 

Answers and Replies

  • #2
22,097
3,279
Looks good to me!!

And it's indeed

[tex](TU)(x)=T(U(x))[/tex]
 

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