Solve the following system of equations using Gauss Elimination with the application of scaling and pivoting

$($round all computations to five decimals$).$

$1\mathrm{.}2$t $+2\mathrm{.}9$u $+2\mathrm{.}2$v $14\mathrm{.}5=0$

$3\mathrm{.}1$t $+4\mathrm{.}2$u $+7\mathrm{.}1$v $40\mathrm{.}2=0$

$2\mathrm{.}4$t $+4\mathrm{.}1$u $+3\mathrm{.}2$v $21\mathrm{.}8=0$

Hint: You do not need to develop a program for this problem. Solve it manually and submit.

Problem #$2(75\%)$:

Develop a computer program to solve the following system of equations $($employ initial guesses of $0\mathrm{.}0$ for all

unknowns$)$:

using the following two methods:

$($a$)$ Gauss$-$Seidel

$($b$)$ Jacobi

Perform iterations until the approximation error is $<0\mathrm{.}00001$ and then comment on the obtained results.

Note: For this problem, it is optional to use MatLab or any programming language $($e$.$g$.,$ C$/$C$++,$ Octave,

Python, Java...etc.$).$ However, you are not allowed to use any built$-$in functions in MatLab that are not

available in the other compilers.

Assignment #$2$ Deliverables:

Assignment to be submitted on D$2$L $($Assessments$/$Dropbox$/$Assignment #$2)$ with a file name as:

$$Last Name$\_$First Name$\_$UCID$\_$Group Number$\_$Assignment $2$ and it should include the following:

$$ The full solution of Problem #$1$ with all intermediate steps.

$$ Your source code and the program output for Problem #$2($i$.$e$.,$ solution and approximation error for each

iteration$).$ Note that your code must be working and providing results $($solution$,$ approximation error,

termination criterion...etc.$)$ for full marks.