A scientific experiment requires that the temperature distribution on a thin square metalic plate be carefully monitored. However the physical constraints of the experiment only allow that temperature sensors be placed at the four corners of the plate (red nodes in the figure below). To deal with this problem, the researchers have decided to estimate the temperatures at the remaining 12 points on a 4x4 grid (white nodes in the figure), by assuming that the temperature of any unmeasured node is the average of its immediate neighbors. So for example, the temperature at node 1 equals the average of the temperatures of nodes 0, 2, and 5. the temperature at node 5 equals the average of the temperatures of nodes 4, 1, 6, and 9. Note that this is only true for white nodes; the temperatures at red nodes are given and may not follow this rule. In this exercise we use the tools of linear algebra to compute the twelve missing temperatures.. Each node is identified either by its coordinates (e.g. (2,1)) or by its index (e.g 9). These are shown in the figure. The coordinate labels appear next to the node, while the indexes are inside the node