Consider an economy having three industrial sectors: light industry (its output denoted by yl),heavy industry(its output denoted by Y2) and agriculture (its output denoted by y;). There are three factors of production: labour (1), capital (k), and energy (e). The input requirement matrix is given by 3 12 A=2 51 l 13 This shows that, for example, to produce one unit of light industry the country need to use 3 units of labour, 1 unit of capital, 2 units of energy. Similarly, one unit of heavy industry is produced by using 2 units of labour, 5 of capital and 1 of energy, and so on. 1. How many units of inputs are required to produce an output of one unit of light industry, two units of heavy industry and three units of agricultural goods? Use matrix algebra to answer this question. Hint: the answer is a multiplication of a matrix and a column vector. 2. The country has 100 units of each input. If it fully uses all the inputs, what would be the output olf the country? Use matrix algebra and an inverse matrix to answer this