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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.
Solution Preview
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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