Let T V W Be A Linear Map And Let X1 Xm And Y1 Yn Be Two Lists Of Vectors In V S

 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 .

 

"Looking for a Similar Assignment? Get Expert Help at an Amazing Discount!"