申論題

3.(14%) Let L be a mapping from vector space V to vector space W .

(d) (2+4%) Let L be linear with A as its matrix representation with respective to bases E = [V₁,...,V_n] and F =[w₁,. ,w_m] for V and W, respectively. (i) Describe a mathematic condition about A that is equivalent to L being onto. (ii) Moreover, show the implication from that condition to L being onto.