Let(adsbygoogle = window.adsbygoogle || []).push({}); Vbe a vector space. If U_{1}and U_{2}are subspaces ofVs.t. U_{1}+U_{2}=Vand U_{1}and U_{1}∩U_{2}= {0_{V}}, then we say that V is the internal direct sum of U_{1}and U_{2}. In this case we write V = U_{1}⊕U_{2}. Show that V is internal direct sum of U_{1}and U_{2}if and only if every vector in V may be written uniquely in the form v_{1}+v_{2}with v_{1}∈U_{1}and v_{2}∈ U_{2}.

What does it mean to be unique? Does it matter if it is unique?

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# I Prove that V is the internal direct sum of two subspaces

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