$29\mathrm{.}2-$ Solve this problem first using $1$ internal node and then using $4$ internal nodes; do not use Liebmann's method but rather solve the matrix equations directly using algebraic methods. Finally, solve for a system of $9$ internal nodes either using

Python to solve the matrix equations.

$29\mathrm{.}2$ Use Liebmann's method to solve for the temperature of the square heated plate in Fig. $29\mathrm{.}4,$ but with the upper boundary condition increased to $150C$ and the left boundary decreased to $50C.$ Use a relaxation factor of $1\mathrm{.}2$ and iterate to ${}_s=1\%.$