Problem 1.1. Recall the convention from chemistry in labelling atoms: a small letter after a capital letter belongs to the capital letter, e.g., Pb is a single atom whereas NO3 refers to the molecule consisting of one atom N and three atoms O. For each of the following chemical equations, write down a linear system whose solutions are the amounts of each molecule so that the reaction is balanced. (You don't need to solve the systems.) (a) Pb(NO3)2+NaClPbCl2+NaNO3 (b) C2H2Cl4+Ca(OH)2C2HCl3+CaCl2+H2O