For a linear transformation, is it always true that T(0)=0? Watch

Brian Moser
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For a linear transformation T: U \rightarrow V, is it always true that T( \underline{0} ) = \underline{0}? I assume this is the case, but I wanted to make certain.

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rayquaza17
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(Original post by Brian Moser)
For a linear transformation T: U \rightarrow V, is it always true that T( \underline{0} ) = \underline{0}? I assume this is the case, but I wanted to make certain.

Thanks


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Yes

There's two proofs of this here: https://proofwiki.org/wiki/Linear_Tr...to_Zero_Vector
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Smaug123
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(Original post by Brian Moser)
For a linear transformation T: U \rightarrow V, is it always true that T( \underline{0} ) = \underline{0}? I assume this is the case, but I wanted to make certain.

Thanks


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Notice that "kernel of some linear map U to V" is equivalent to "subspace of U", and since all subspaces contain 0, so too must all kernels.
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