Question

Find the missing number in the following: \[ \beginbmatrix 2 & 3 & 1
1 & 2 & -1
? & 3 & 4 \endbmatrix \]

• A. 5
• B. 2
• C. 1
• D. 4

Hint:

In missing number puzzles with matrices, check for arithmetic relationships row-wise or column-wise, often involving constant differences.

Answer 1

The Correct Option is A

We need to find the missing number in the first column, third row.
Looking closely at the given matrix, it seems that each row might be following a pattern or sum involving its elements.
Step 1: Check if row sums follow a constant:
Row 1: $2 + 3 + 1 = 6$
Row 2: $1 + 2 + (-1) = 2$ — not constant, so this is not the pattern.
Step 2: Check if there’s a multiplication-sum relation:
Sometimes, first element × second element = third element, but here:
Row 1: $2 \times 3 = 6$ (not equal to 1), so no.
Step 3: Check column-based relation:
Column 1: 2, 1, ?
Column 2: 3, 2, 3
Column 3: 1, -1, 4
Observe: In each row, (first element) + (second element) = (third element) + constant. Let’s test:
Row 1: $2 + 3 = 5$, and $1$ is 4 less than 5 — constant difference 4?
Row 2: $1 + 2 = 3$, and $-1$ is 4 less than 3 — yes, difference 4.
Thus: First + Second = Third + 4.
Step 4: Apply to Row 3: Let missing number = $x$.
$x + 3 = 4 + 4$
$x + 3 = 8$
$x = 5$
Therefore, the missing number is $\mathbf5$.