Let T: V W be a linear transformation, where V and W are finite dimehsional. Show
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Show that T is onto if and only if there exists a linear transformation S: W → V with TS = 1w A [Let {e1,..., er ,..., en} be a basis of V such that {er+1,..., en] is a basis of ker T. Use Theorem 5 §7.2 and Theorems 2 and 3, §7.1.]
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If TS 1 W then given w in W TSw w so T is onto Con...View the full answer
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