Question

The matrix shows a table ot values at the points of a grid of a tunction u(x,y) solving the Laplace equation uxx​+uvy​=0 over a rectangle. Which of these options would be the best estimate for the missing entry ??? in the table? ⎣⎡​00.030.110.220.35​0.220.240.30.380.47​0.410.420.460.520.59​0.56???0.60.640.7​0.690.70.720.760.8​⎦⎤​

Answer 1

The missing entry in the table can be estimated by finding the average value of the numbers in the surrounding entries. The best estimate for the missing entry is 0.51.

Step-by-step explanation:

The missing entry in the table can be estimated by finding the average value of the numbers in the surrounding entries. Let's consider the entry located in the third row, second column (the missing entry is denoted as ???). We can take the average of the numbers in the same row and the same column as the missing entry. In this case, the average would be (0.640 + 0.42 + 0.24 + 0.7) / 4 = 0.51. Therefore, the best estimate for the missing entry would be 0.51.