Assume that we have the following inter-industry transaction matrix for a simple 3-sector economy S1, S2 and S3 Z = 350 0 0 50 250 175 200 150 550 Let us also assume that the total production of each sector is given by X = 1400 1000 1100 Let us now define the matrix matrix X, such that X = 1400 1000 1100 Let us now define the matrix matrix X, such that 1400 0 0 0 0 1100 0 x = 1000 0 a) Using R, create the vector x and use the diag function to create the matrix x b) Use the Z matrix and the matrix to find the technical coefficient matrix A for this simplified economy. A single operation should be enough. Hint: Think about the algebraic properties of diagonal matrices!.