Consider a mixture of $CO,H_2,$ and $C{H}_4$ that is fed into a furnace with $O_2$ and produces $CO,C{O}_2,$ and

$H_{2}O.$ The following chemical reactions have been suggested to account for the products that form.

$CO+\frac{1}{2}{O}_{2}C{O}_2(1)$

$H_2+\frac{1}{2}{O}_2{H}_{2}O(2)$

$C{H}_4+2O_{2}C{O}_2+2H_{2}O(3)$

$C{H}_4+\frac{3}{2}{O}_{2}CO+2H_{2}O(4)$

$($a$)$ Are these reactions linearly independent? What is the number of linearly independent

reactions, $n?$

$($b$)$ List all sets of $n$ linearly independent reactions. Which reaction is included in all of the linearly

independent sets of reactions? Why?Consider a mixture of CO$,$ H$2,$ and CH$4$ that is fed into a furnace with $02$ and produces CO$,$ CO$2,$ and H$20.$ The following chemical reactions have been suggested to account for the products that form. $2$ CH$42$O$2$CO$22$H$2$O CH$4+02-$CO $+2$H$2$O $($a$)$ Are these reactions linearly independent? How many reactions comprise a linearly independent set? $($b$)$ List all sets of linearly independent reactions. Which reaction is included in all of the linearly independent sets of reactions? Why?