1. (8 marks.) Consider a simple IS-LM model of a closed economy with no government sector, in which the price level is fixed. The endogenous variables in such a model are the equilibrium goods output (and income), which we will denote by Y, and the equilibrium real (an, given the fixed price level, nominal) interest rate, which we will denote by r. Suppose that the locus of goods market equilibrium combinations (that is, the IS curve) for this economy is described by the equation 0.3Y + 100r = 252, and the locus of money market equilibrium combinations (that is, the LM curve) for this economy is described by the equation 0.25Y - 200r = 176. (a) Express this system of equations as a matrix equation of the form Ar = b for which r = (Y,r) ". (b) Find the cofactor for each of the elements of the coefficient matrix in that system of equations. (Explicitly calculate each of these cofactors. Do not use any "short-cut" approaches to obtain them.) (c) Find the cofactor matrix of the coefficient matrix in that system of equations. (d) Use the relevant cofactor matrix to find adjoint matrix of the coefficient matrix in that system of equations. (e) Use the relevant adjoint matrix to obtain the inverse coefficient matrix for that matrix equation. (f) Use the relevant inverse coefficient matrix to find the equilibrium goods output and the equilibrium real interest rate for this economy