Composition of linear transformations

Thread starter krozer
Start date Oct 25, 2011
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Composition Linear Linear transformations Transformations

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Two linear operators T and U on R^2 are defined as T(x1,x2)=(0,x2) and U(x1,x2)=(x2,0). The composition TU results in the zero operator, as TU(x1,x2)=T(U(x1,x2))=(0,0). However, the composition UT does not equal zero, demonstrating UT(x1,x2)=U(T(x1,x2))=(x2,0). The discussion clarifies the correct order of operations for composition, confirming that (TU)(x)=T(U(x)). This example effectively illustrates the properties of linear transformations in relation to their compositions.

Oct 25, 2011

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)]

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Oct 25, 2011

micromass

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Looks good to me!

And it's indeed

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

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