1. The problem is to find the missing number represented by ?? in the given matrix: 49 03 27 95 37 01 87 16 83 77 39 98 50 93 47 72 39 16 24 79 13 49 27 01 53 71 97 10 06 54 48 31 ?? 2. To solve this, we look for a pattern in the rows or columns. 3. Let's check if the sum of each row is consistent: Row 1 sum: $49 + 3 + 27 + 95 + 37 + 1 + 87 = 299$ Row 2 sum: $16 + 83 + 77 + 39 + 98 + 50 + 93 = 456$ Row 3 sum: $47 + 72 + 39 + 16 + 24 + 79 + 13 = 290$ Row 4 sum: $49 + 27 + 1 + 53 + 71 + 97 + 10 = 308$ 4. The sums are not equal, so no constant row sum. 5. Check columns sums for the first 6 rows (since last row has missing number): Column 1: $49 + 16 + 47 + 49 + 6 = 167$ Column 2: $3 + 83 + 72 + 27 + 54 = 239$ Column 3: $27 + 77 + 39 + 1 + 48 = 192$ Column 4: $95 + 39 + 16 + 53 + 31 = 234$ Column 5: $37 + 98 + 24 + 71 + ?? = ?$ Column 6: $1 + 50 + 79 + 97 + ? = ?$ Column 7: $87 + 93 + 13 + 10 + ? = ?$ 6. Since the last row has only 5 numbers, it seems the matrix is incomplete or the last row is shorter. 7. Alternatively, check if the last row is missing two numbers after 31, or if ?? is the 5th number. 8. Assuming ?? is the 5th number in the last row, and the last row has 6 numbers total, the pattern is unclear. 9. Without a clear pattern or rule, the missing number cannot be determined from the given data. Final answer: Cannot determine the missing number ?? with the given information.