Solve the following grid puzzle: Fill in the missing numbers given row and column sums.

The problem presents two grids. The first grid appears to be an example, and the second grid is the one to be solved. The numbers outside the grids represent the sums of the numbers in the corresponding rows and columns.

Let's analyze the second grid first, as its given numbers are clearer and it seems to follow a standard pattern.
Let the unknown numbers in the second grid be $x_1$ and $x_2$.
The grid is:

$$\begin{bmatrix} 5 & 3 \\ x_1 & x_2 \end{bmatrix}$$

The sums are given as:

• Top row sum: $5 + 3 = 8$. This matches the 8 given on the right side of the top row