System Of Equation

p {margin: 0; padding: 0;} No Date Application : System of equations 1) A general Form matrix of a system of linear equations Axe d where A = matrix of parameters x = column vector of endogenus variabels d 1 column vector of exogenus variables and constants 2) Solve for x all a12 aim X d. are A22 a m X2 dz an, anz anm Yn dn Solution of a General- equation System 1) Theorem Given A (m xn) If A has a right - inverse, then the equation Ax = d has at least one solution for everyday d (mx1) proof Rick an arbitrary d. Let H be a right-inverse (so AH = Im) Define x = Hd This Ax - A Hd= Imd =d x* i a solution 2) Given A (mxn) If A has a left-inverse, then the equation Ax=d has at most one solution For everyday (mvl) That is, if Ax = d has a solution x for a particular d. then x is unique