Given the following chemical reactions. Balance these equations using MATLAB. You may add auxiliary equations $($if needed$).$ Ensure that your final column vectors consist of only integers.

$x_{1}C{r}_2{O}_7^{2-}+x_{2}F{e}^{2+}+x_3{H}^{+}{x}_{4}C{r}^{3+}+x_{5}F{e}^{3+}+x_6{H}_{2}O.$

Hint: In addition to balancing the four elements $(Cr,O,Fe,$ and $H),$ charge must be conserved as well, e$.$g$.,$ for this equation: $-2x_1+2x_2+x_3=3x_4+3x_5.$

$x_1{P}_2{I}_4+x_2{P}_4+x_3{H}_{2}O{x}_{4}P{H}_{4}I+x_5{H}_{3}P{O}_4.$

$x_{1}Mn{O}_4^{-}+x_2{H}_2{O}_2+x_3{H}^{+}{x}_{4}M{n}^{2+}+x_5{O}_2+x_6{H}_{2}O.$

Hint: Assume $x_6=6$ and choose the auxiliary equation so that you get positive integers as the coefficients without the need for scaling. You can start with $x_1=1$ and keep incrementing $x_1$ until you get a valid solution.

$x_1$CuS$+x_{2}N{O}_3^{-}+x_3{H}^{+}{x}_{4}C{u}^{2+}+x_{5}S{O}_4^{2-}+x_{6}NO+x_7{H}_{2}O.$

All the solution vectors should be in the form of a column vectors.