a$.)(10$ pts$)$ Consider the following system of linear equations.

$22+53=1$

$21+2+3=1$

$31+2=2$

i$.)$ Solve the system of equations using Gauss$-$Elimination with Partial Pivoting

Method. Perform two iterations by hand.

ii$.)$Solve the system of equations using Gauss$-$Seidel Iteration Method with initial

guesses

$$

$(0)000$ T

x $=$

$.$ Take $=0\mathrm{.}01\%($percentage approximate relative

error$).$ Perform two iterations by hand. Give your comments.

b$.)(5$ pts$)$ Solve the same system of linear equations using Gauss$-$Elimination with

Partial Pivoting algorithm and Gauss$-$Seidel Iteration algorithm in MATLAB $($not

use built$-$in functions such as $$linsolve$).$ Compare your results that are obtained in

the $$Part a