1. The problem involves analyzing a 9x9 grid with given cell values and corresponding row and column sums. 2. We want to verify the consistency of the sums and understand the distribution of values in the matrix. 3. The matrix cells contain numbers representing weights or counts, and the row sums and column sums are provided. 4. To check consistency, sum each row's cell values and compare with the given row sums. 5. Similarly, sum each column's cell values and compare with the given column sums. 6. The formula for sum verification is: $$\text{Sum of row } i = \sum_{j=1}^9 a_{ij}$$ and $$\text{Sum of column } j = \sum_{i=1}^9 a_{ij}$$ where $a_{ij}$ is the value in row $i$, column $j$. 7. By verifying these sums, we confirm the accuracy and completeness of the data. 8. This process helps in understanding the distribution and can be used for further analysis like optimization or pattern recognition. 9. Since the problem is about matrix sums and verification, the subject is linear algebra.