Matrices · 2.1.2
Order and elements of a matrix
The order of a matrix is written as (number of rows) × (number of columns). Students must count rows and columns correctly to state the order, then locate a specific element using its row-column position, for example a₂₃ means the element found in row 2, column 3.
The official learning standard (2.1.2)
“Determine the order of a matrix, hence identify certain elements in a matrix.”
What it means
The order of a matrix is written as (number of rows) × (number of columns). Students must count rows and columns correctly to state the order, then locate a specific element using its row-column position, for example a₂₃ means the element found in row 2, column 3.
How it is examined
A common Paper 1 objective item, given a matrix, state its order or identify the element aij. It also occasionally appears as the first sub-part of a Paper 2 structured question, setting up matrix operations that follow in later parts of the same question.
Worked example
Given matrix A = [[2, -1, 5], [0, 3, 4]], state the order of A and find the element a₂₃.
- Count the rows: 2 rows.
- Count the columns: 3 columns.
- Order = rows × columns = 2 × 3.
- Element a₂₃ is in row 2, column 3: value = 4.
Source:DSKP KSSM Mathematics Form 4 and 5 (Versi English)
Frequently asked questions
How do I remember the order rows-then-columns?
Use "RC" as a memory aid, Rows come before Columns, just like reading a book from top row to side column. Practise on several matrices, always counting rows first, then columns, until stating the order becomes automatic in an exam.
What does a₃₁ mean?
It means the element found in row 3, column 1 of matrix A. The first subscript is always the row number, and the second subscript is always the column number, so a₃₁ is different from a₁₃ unless the matrix happens to be symmetric.
Can two matrices with the same order have different elements?
Yes, order only describes the shape (rows × columns) of a matrix, not its content. Two matrices can both be 2×2 but contain completely different numbers; matrices are only equal when both their order and every corresponding element match exactly.