MATH LINEAR ALEGRA $(341)$ SOLVE SHOW WORK WILL UPVOTE.

Question $1.$ In the study of heat transfer, it is important to determine the steady$-$state temperature distribution of points along a thin plate when the boundary temperature of the plate is known and held fixed. Consider the grid of points along a thing plate shown below. We assume that the plate loses no heat to its ambient surroundings and use the principle that each node temperature is the average of its neighbors. For example at an internal node we have,

$T_1=\frac{1}{4}[T_2+B_2+B_{12}+T_4]$

Write a system of equations that describes the temperature of the four internal nodes, $T_1,$dots,$T_4.$

ALSO PLEASE $*$#$2*$SOLVE SYSTEM OF EQUATION?! WILL UPVOTE IF ANSWER:$)$