Question $1$: Solve the system of equations given below using the Gauss$-$Seidel Method for three iterations.

$4x-y+z=7$

$x+3y-z=4$

$x-y+4z=5$

$($a$)$ Start with the initial guess $x_0=[0,0,0{]}^T.$

$($b$)$ Perform the first three iterations manually.

$($c$)$ Verify your solution using a Python implementation.