Consider one$-$dimensional heat conduction in a plane wall of thickness L with uniform

heat generation e$^()$ and constant thermal conductivity k with a mesh size of $\backslash$Delta x$=($L$)/(7)$ and

nodes $0,1,2,$dots,$7$ in the x$-$direction. Heat flux q$^()$ occurs on the left side of wall $($x$=0),$

and convection takes place on the right side of wall $($x$=$L$)$ to the ambient at T$\_(\backslash$infty $)$ with the

convective heat transfer coefficient h$.$ Set up a linear system equation in the form of

$[$A$]\{$T$\}=\{$b$\},$ where $[$A$]$ is an $8\backslash$times $8$ square matrix, $\{$T$\}$ is an $8\backslash$times $1$ vector that is $\{($T$\_(0)),($T$\_(1)),($dots$)$:$\},$

T$\_(7)(10$ pts$).$