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

[tex](\forall x \in U \cap W) S(x)=T(x)[/tex]

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

My thought is to choose the linear transformation [tex]F=S+T[/tex] 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

[tex](\forall x \in U \cap W) S(x)=T(x)[/tex]

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

My thought is to choose the linear transformation [tex]F=S+T[/tex] 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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