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QUESTION
Let T : V W be a linear map, and let x1,.,xm and y1,.,yn be two lists of vectors in V . Suppose that (a) x1,.,xm generate KerT, and (b) T(y1),.,T(yn)...
Let T : V → W be a linear map, and let x1,...,xm and y1,...,yn be two lists of vectors in V . Suppose that
(a) x1,...,xm generate KerT, and (b) T(y1),...,T(yn) generate W.
Show that the list x1,...,xm,y1,...,yn generates V .
