Find the correct solution through code

Mass spectrometry analysis gives a series of peak height readings for various ion masses. For each peak,

the height h$\_($i$)$j j$^($th $)$ component

with per unit concentration p$\_($j$)$ makes the contribution c$\_($ij$)$ to the i$^($th$)$ peak, so that the following relation

holds.

h$\_($i$)=\backslash$sum$\_($j$=1)^$n c$\_($ij$)$p$\_($j$),$

where n is the number of components present. Carnahan $(1964)$ gives the c$\_($ij$)$ values shown in the table

below:

If a sample had measured peak heights h$\_(1)=5\mathrm{.}20,$h$\_(2)=61\mathrm{.}7,$h$\_(3)=149\mathrm{.}2,$h$\_(4)=79\mathrm{.}4,$ and h$\_(5)=89\mathrm{.}3.$

Calculate the values of p$\_($j$)$ for each component. The total of all the p$\_($j$)$ values was $51\mathrm{.}53.$ Use Jacobi's

and Gauss$-$Seidal iteration approaches, till adjacent iterations is within $10^(-6).$

Requirements: Rearrange the measurements to take advantages of the principle and strength of each

iteration method.