Find the missing number : [[?, 13, 49], [9, 17, 69], [13, 11, 59]]

The correct answer is (B) 5.

• Principle: In this matrix problem, we need to establish a mathematical relationship between the numbers in each row or column. Let us analyze the rows where the third column contains the resultant values formed by the first two columns.
• Calculation: Examining Row 2: 9 × 4 + 17 × 2 = 36 + 34 = 70 (approximate to 69 or check alternative rule). Let us check another rule: Row 2: (9 + 17) × 2.5 or column-wise operations. Let us check column operations: Column 3 values are 49, 69, 59. Notice the pattern in Column 3: differences are 20 and 10. Let us test row formula First Number × 3 + Second Number × 2: For Row 2: 9 × 3 + 17 × 2 = 27 + 34 = 61 (incorrect). Let us test First Number × 4 + Second Number × 1: Row 2: 9 × 4 + 17 × 1 = 53. Let us test First Number + Second Number × 3: Row 2: 9 + 17 × 3 = 60. Let us re-examine standard matrix logic: (First Number × 2) + Second Number + constant or (First Number + Second Number) × factor. Let us check Row 2: 9 + 17 = 26, 69 - 26 = 43. Let us check row formula (First Number × 3) + Second Number + something. Actually, check Row 3: 13 + 11 = 24, 59 - 24 = 35. Let us test alternative relationship: First Number × 3 + Second Number + something. Let us check Option (B) 5 for the first row: If ? = 5, let us test rule: Row 1: 5 × 3 + 13 = 28, 49 - 28 = 21. Let us check (First Number × 2) + (Second Number × 2) + .... Let us check formula: First Number × 2 + Second Number × 3 -> Row 2: 9 × 2 + 17 × 3 = 18 + 51 = 69. Let us apply this exact verified formula (Column 1 × 2 + Column 2 × 3 = Column 3) to all rows: Row 2: 9 × 2 + 17 × 3 = 18 + 51 = 69. Row 3: 13 × 2 + 11 × 3 = 26 + 33 = 59. Row 1: ? × 2 + 13 × 3 = 49 ⇒ ? × 2 + 39 = 49 ⇒ ? × 2 = 10 ⇒ ? = 5.
• Verification: The derived missing number is 5, which perfectly matches option (B). Other options (9, 7, 11) fail to satisfy the established row-wise linear equation (Col 1 × 2) + (Col 2 × 3) = Col 3.