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Linear Algebra. Can you please add explanations as far as possible? Problem 16. Show that for any 9 E L(V,C) and u E V with

Linear Algebra. Can you please add explanations as far as possible?

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Problem 16. Show that for any 9 E L(V,C) and u E V with 3(a) a 0: V=nMg${Au:AEC}. [10 marks] Problem 18. Suppose V and W are niteudimensional and T E L(V, W) Show that with respect to each choice of bases of V and W, the matrix of T has at least dim range T nonzero entries. [10 marks]

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