Problem $3$: Ammonia and Oxygen react as follows.

$N{H}_3+{}_1{O}_2{}_{2}N{O}_2+{}_3{H}_{2}O$

$($a$)$ You are required to determine the stoichiometry $\{{}_1,{}_2,{}_3\}$ by doing atomic balances and

writing this as a linear system of equations $A=b,$ where $A-=33$ matrix; $b-=$

$31,$ and $=31($unknowns$).$ Show details of your system of equations.

$($b$)$ Solve the system by hand using Gaussian Elimination. $[$Hint: to do an atomic balance on

an atom say $N,$ you need to count the number of $N$ atoms on both sides of the chemical

reaction.$]$