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Let U and W be subspaces of a finite dimensional vector space V such that V=U⊕W....

Let U and W be subspaces of a finite dimensional vector space V such that V=U⊕W. For any x∈V write x=u+w where u∈U and w∈W. Let R:U→U and S:W→W be linear transformations and define T:V→V by Tx=Ru+Sw

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Show that detT=detRdetS

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