Question: Let T: V W be a linear transformation, and let {e1..., er, er+1,..., en) be any basis of V such that {er+1,..., en} is

Let T: V → W be a linear transformation, and let {e1..., er, er+1,..., en) be any basis of V such that {er+1,..., en} is a basis of ker T. Show that im T = span{e1 ,..., er}.

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Theorem 5 Section 72 shows that Te 1 Te 2 Te r is a basis of im T Write ... View full answer

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