# How this defines a linear transformation

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## Main Question or Discussion Point

Admit that $$V$$ is a linear space about $$\mathbb{R}$$ and that U and W are subspaces of V. Suppose that $$S: U \rightarrow Y$$ and $$T: W \rightarrow Y$$ are two linear transformations that satisfy the property:

$$(\forall x \in U \cap W) S(x)=T(x)$$

Define a linear transformation $$F: U+W \rightarrow Y$$ that matches with S for values in U and matches with T with values in W.

My thought is to choose the linear transformation $$F=S+T$$ because it will be the union of both transformation, right? But we have the problem that when our objects are in the intersection of both space we will get to F = 2S instead of S

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Stephen Tashi
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Admit that ##V## is a linear space about ##\mathbb{R}## and that U and W are subspaces of V. Suppose that ##S: U \rightarrow Y## and ##T: W \rightarrow Y## are two linear transformations that satisfy the property:

##(\forall x \in U \cap W)\ S(x)=T(x)##

Define a linear transformation ##F##: ## U+W \rightarrow Y## that matches with S for values in U and matches with T with values in W.
Are you asking whether it is possible to define such a linear transformaton ?

My thought is to choose the linear transformation ##F=S+T## because it will be the union of both transformation, right? But we have the problem that when our objects are in the intersection of both space we will get to F = 2S instead of S

Hello Stephen!

Thanks, I edited my question.

No, I know it's possible to define the linear transformation I'm asking what should be the linear transformation and how can I get there :)

jbunniii