Matrix P is given by #((4,7),(5,8))#(a) Find #P^(-1) #(b) Two institutions, Elimu and Somo, purchased beans at sh. b per bag and maize at sh. m per bag. Elimu purchased 8 bags of beans and 14 bags of maize for sh. 47,600. Somo purchased 10 bags of beans and 16 bags of maize for sh. 57,400. (i) Form a matrix equation to represent the information above. (ii) Use the matrix #P^(-1)# to find the prices of one bag of each item. (c) The price of beans later went up by 5% and that of maize remained constant. Elimu bought the same quantity of beans but spend the same total amount of money as before on the two items. State the new ratio of beans to maize.
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