5. [15 points) For the matter of prudent diversification, an investor wishes to have his $100 of wealth invested as $50 in the Canadian economy, $30 in the U.S. economy, and $20 in the English economy. Although he can purchase the shares of firms that are based in Canada, the U.S. and England, it happens that each of these firms conducts some of its operations through foreign subsidiaries. In particular, the Canadian based firm (C) has 50% of its operations in Canada but 50% in the U.S., the U.S. based firm (U) has 50% of its operations in the U.S. but 50% in England, and the England based firm (E) has 50% of its operations in England but 50% in Canada. (a) The problem for the investor is to determine the proper amounts to invest in each of these three firms to achieve his desired investment in the three economies. Write down a matrix equation that represents the problem he has to solve. Let the amounts invested in the three firms be represented by the column vector: [5 points) XT = [ CUE] (b) Use matrix inversion to solve for the amount that he should invest in each firm simultaneously [10 points]