$2\mathrm{.}4.$ A flat square plate shown in Figure $1,$ its sides held at constant temperatures.

Each grey dot represents a node, and the temperature at each node is

assumed to be given by the average temperatures of adjacent nodes.

Figure $1.$ Flat square plate with heat transfer.

Find the temperature at each node $T_1,T_2,T_3,$ and $T_4,$ where:

COMPUTATIONAL TECHNIQUES $$

$T_1=\frac{1}{4}(30+15+T_2+T_3),T_2=\frac{1}{4}(T_1+15+20+T_4),T_3=\frac{1}{4}(30+T_1+T_4+25)$ and

$T_4=\frac{1}{4}(T_3+T_2+20+25)$

$2\mathrm{.}5.$ Calculate the expression below and fix to $5$ significant figures:

Hint use the colon notation for the vectors.

$R=\frac{r(-xt+y{t}^2)}{15}-s^2(y-0\mathrm{.}5x^2)t$

where are scalar components $r=1\mathrm{.}6{10}^3$ and $s=14\mathrm{.}2,t=[1,2,3,4,5]$;$x=$

$2,4,6,8,10$ and $y=[3,6\mathrm{.}9,12,15]$ are vectors.