Final Answer:
The possible orders for a matrix with 12 elements are: 1×12, 2×6, 3×4, 4×3, 6×2, 12×1.
For 8 elements: 1×8, 2×4, 4×2, 8×1.
For 7 elements: 1×7, 7×1.
For 5 elements: 1×5, 5×1.
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Explanation:
- A matrix order means how many rows and columns it has, like “rows × columns”.
- The total number of elements = rows × columns.
- So we need to find all pairs of whole numbers that multiply to give the total elements.
For 12 elements:
Think of all multiplication pairs:
1 × 12 = 12 → so 1 row, 12 columns → 1×12
2 × 6 = 12 → 2×6
3 × 4 = 12 → 3×4
Also, flip them: 4×3, 6×2, 12×1.
That’s 6 possible orders.
For 8 elements:
1×8, 2×4, 4×2, 8×1 → 4 orders.
For 7 elements:
7 is prime → only 1×7 and 7×1 → 2 orders.
For 5 elements:
Same as 7 → only 1×5 and 5×1 → 2 orders.
That’s it! Just list all factor pairs.
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Parent Tip: Review the logic above to help your child master the concept of matrices worksheet.
