Question: 4 . Let I EC ( V , W ) and S' be a subspace of V. Define : I ; V / S -

4 . Let I EC ( V , W ) and S' be a subspace of V. Define : I" ; V / S - V / S' such that I" ( V + 5" ) = I ( v ) + 5. ( 1 ) Verify that I' is well - defined . !' ( 2) Verify that I" is a linear transformation .\\ ( 3) Find N ( I') and R ( I'). 5 . Let V be a complex vector space and A E [ ( V ). Assume that A has K distinct eigenvalues 1 1 . .... Ax. Show that V = GEN, D ... ` GEAR`

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