onsider the following linear system

$3$x$+2$y$4$z$$w$=9$

$7$x$3$y$5$z$+2$w$=6$

x$+$y$+$z$+$w$=10$

$2$x$$y$+5$z$3$w$=3$

$$

a$)$ Solve the system using Matlab$/$Octave rref, backslash, and the inverse commands. Call the solution X$.[3]$ b$)$ Compute the spectral radius of the coefficient matrix. $[2]$ c$)$ Use the $2-$norm to Compute the condition number of the coefficient matrix. What the number tells you about the matrix. $[2]$ d$)$ Use Matlab$/$Octave code to solve the system using the Jacobi method starting with initial value X

$(0)$

$=(0\mathrm{.}5,0\mathrm{.}5,0\mathrm{.}5,0\mathrm{.}5,0\mathrm{.}5).$ Call the solution XJ$.$ Print $10$ iterations. $[4]$ e$)$ Use Matlab$/$Octave code to solve the system using the Gauss$-$Seidel method starting with initial value X

$(0)$

$=(0\mathrm{.}5,0\mathrm{.}5,0\mathrm{.}5,0\mathrm{.}5,0\mathrm{.}5).$ Call the solution XGS$.$ Print $10$ iterations. $[4]$ f$)$ Use Matiab$/$Octave code to compute the $\backslash |$ X$$XJ$\backslash |$

$2$

$$

and $\backslash |$ X$$XGS$\backslash |$

$2$

$$

for the errors in the approximation. $[3]$ g$)$ Are the two numerical methods converging to the solution? Which method is better to use. Justify your answer. $[2]$