MathIsland · We are all mathematicians.
Matrices
Read matrix entries and operations while preserving the roles of their positions.
Start with the picture
A matrix preserves positional meaning; each operation has its own dimension and pairing rules.
Check with another example
1. A has rows (1,2) and (3,4). What is a₂₁?
- 3
- 2
- 4
My reason
2. With quantities (2,3) and unit prices (1000,2000), what is the total?
- 5000 won
- 8000 won
- 12000 won
My reason
3. What are the dimensions of AB if A is 2×3 and B is 3×4?
- 6×12
- 3×3
- 2×4
My reason
Explain in your own words
Why should we know the meaning of rows and columns, not just their numbers?
Answers and reasons
1. 3
Row 2, column 1 gives 3. Indices are ordered row, then column.
2. 8000 won
2×1000+3×2000=8000. We multiplied corresponding entries, then added.
3. 2×4
Each of A's two rows pairs with each of B's four columns.
Positions distinguish objects and units. Mixing their roles can pair quantities and prices incorrectly.