Hello everyone,
I need help plz
Find a Counter example for:
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).
Thank you
There is no counterexample for this since it's true: $\displaystyle y=Tx+Ux \in R(T)+R(U)$. The other inclusion is false: take $\displaystyle T,U: V \rightarrow V$ with $\displaystyle T=id_V$ and $\displaystyle U=-id_V$ then $\displaystyle R(T+U)= \{0 \}$ and $\displaystyle R(T)+R(U)=V$