Consider the following linear system

$4x_1+x_2-x_3+x_4=-2$

$x_1^{}+4x_2-x_3-x_4=-1$

$-x_1-x_2+5x_3+x_4=0$

$x_1-x_2+x_3+3x_4=1$

a$)$ Solve the system using Matlab$/$Octave rref, backslash, and the inverse commands. Call the

solution $x.$

b$)$ Use Matlab$/$Octave code to solve the system using the Jacobi method, starting with the initial

value $x^{(0)}=(0,0,0,0).$ Call the solution $xJ.$ Print $5$ iterations.

c$)$ Use Matlab$/$Octave code to solve the system using the Gauss$-$Seidel method, starting with the

initial value $\{$:$x^{(0)}=(0,0,0,0)).$ Call the solution $xGS.$ Print $5$ iterations.

d$)$ Use Matlab$/$Octave code to compute the $||x-xJ|{|}_2$ and $||x-xGS|{|}_2$ for the errors in the

approximation.

e$)$ Are the two numerical methods converging to the solution? Which method is better to use?

Justify your answer.

solve the questions using octave or matlab program