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Show that the following is not a theorem by finding a counter example.

If T and U are linear transformations from V to W and W are vector space then R(T+U) subset of or equal R(T) + R(U).

R(T) = the range of the linear transformation T

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Solution Summary

A counter example is included. The expert shows that a linear transformation is not a theorem by finding a counter example.

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the claim is actually (obviously) true:

if x is in V, then (T + U)(x) = T(x) + U(x) *is* contained in T(V) ...

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