Attached is an economic test on international trade kindly help me get the solution

6. Factor Content of Trade and Factor Prices There are three goods and three factors. Country 1's output vector in the free trade equilibrium is X = (20, 20, 10). The world output vector (including country 1) is X = (100, 200, 200). The output price vector is P = (1, 6/5, 1). All countries have an identical constant-returns fixed-coefficient technology, whose input-output matrix is 3 A = where the element in row i and column / denotes the input of factor i per unit output of good j. All countries have identical homothetic preferences and trade is balanced. (a) Calculate country I's pattern of goods trade, and its factor content. Calculate the factor prices. (b) Does the Stolper-Samuelson theorem hold locally? That is, suppose the price of good 1 increases. Is it the case that all three factors will either benefit or lose unambiguously, no matter what their consumption patterns happen to be? If not, which factor's real reward is affected ambiguously? (c) Now alter the assumptions so that the world factor endowments remain unchanged, but those of country 1 become (150, 350, 250). Is this consistent with factor price equalization