Two Linear transformations $L$ and $K$ are equal if and only if they have same kernel and same images.
I have no idea how to prove or give a counter example.
Can someone give me a hint to the right way!
Thanks
2026-04-25 00:08:18.1777075698
Equality of two linear transformations
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Not true. Take $L,K\colon\mathbb{R}\longrightarrow\mathbb{R}$ defined by $L(x)=x$ and $K(x)=2x$. They are different but they have the same kernels and the same images.