I. Chemistry: A. Consider the chemical reaction: PbN6+CrMn2O8Pb3O4+Cr2O3+MnO2+NO a. Let a,b,c,d,ef denote the number of molecules of each type that are needed to balance the chemical equation above. So, aPbN6+bCrMn2O8cPb3O4+dCr2O3+eMnO2+fNO2 For this equation to balance, there need to be the same number of oxygen atoms ohi both sides of the equation. Write down the equation that the variables a,b,c,d,e,f must satisfy in order for the number of oxygen atoms on both sides of the equation to be equal. Now write down a similar equation for each of the other four elements, so that you have five equations altogether. b. Move all of the unknowns to the left. You now have a homogeneous system of five linear equations. Use MATLAB to help find the general solution to the system. Record the final solution to the system on your answer sheet. c. There should be infinitely many solutions. Which one makes the most sense in terms of balancing this chemical equation? Explain your reasoning. (HINT: you will probably want to type format ('rat') into MATLAB so that computations are given in fractions rather than decimals.)