Matrix Notation, Order and Entries
Ages 13–15Difficulty adapts to you
Matrix Notation, Order and Entries
A matrix is a rectangular arrangement of numbers or symbols. The horizontal lines are rows and the vertical lines are columns. We write the order as rows × columns, so the row count always comes first. If A has m rows and n columns, its order is m × n and we write A = [aᵢⱼ], where aᵢⱼ means the entry in row i and column j. Read the first subscript before the second: a₂₃ means row 2, column 3.
Your goals
- ✓You can read matrices, state their order, and locate their entries.
- ✓You can use matrix, order, entry correctly.
- ✓You can count rows first, columns second, then locate the requested row and column.
Words to know
- matrix:
- A rectangular arrangement of values in rows and columns.
- order:
- The number of rows followed by the number of columns.
- entry:
- One value inside a matrix.
Examples
- 1A = 257146 has 2 horizontal rows and 3 vertical columns, so its order is 2 × 3.
- 2For A = 257146, a₂₃ = 6 because it is in row 2, column 3.
- 3The matrix 123456 is not 3 × 2: it has two rows, and each row has three entries, so it is 2 × 3.
- 4If three classes are rows and two terms are columns, 425038414547 has order 3 × 2 and 6 entries.
- 5A missing entry can be recovered from its position: if B = x47y, b₁₁ = −3 and b₂₂ = 8, then x = −3 and y = 8.
Check these
- • Do not reverse the row and column subscripts or count columns first.
- • Keep every number, symbol, label, and unit in its correct place.
- • Show enough working to check how you reached your answer.
Helpful habits
- • Read the whole question before choosing what to do.
- • Show one clear step at a time and check each step.
- • If you are stuck, draw a model, try smaller numbers, or revisit the example.
Now try your own
Create your own matrix notation, order and entries example, solve it, and explain how you checked it.
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