The order of a matrix is its number of rows followed by its number of columns, written rows × columns. An entry is named by its row first, then its column.
This is the first lesson in SPM Mathematics matrices. Everything after it, from adding to solving equations, depends on getting positions right.
How do you read the order?
Count across the horizontal lines first. Those are the rows. Then count the vertical lines, which are the columns.
Take this matrix:
M = | 4 −1 6 |
| 0 3 2 |It has 2 rows and 3 columns, so the order of M is 2 × 3. It has 2 × 3 = 6 entries.
How do you find one entry?
Name the row, then the column. The entry in row 2, column 3 of M is 2. The entry in row 1, column 2 is −1.
A memory trick: think of a cinema ticket. You find the row first, then the seat.
Worked example: a shop stock table
A shop records items sold on two days, in a matrix. The rows are the days and the columns are pens, rulers and erasers.
S = | 12 5 9 |
| 8 11 4 |- The order of S is 2 × 3, because there are 2 days and 3 item types.
- The number of rulers sold on day 2 is in row 2, column 2, so the entry is 11.
- The number of erasers sold on day 1 is in row 1, column 3, so the entry is 9.
If the same information were laid out with the items as rows, the matrix would have order 3 × 2. The numbers are the same, but it is a different matrix.
The mistake that costs marks
A common slip is to write the order as columns × rows, giving 3 × 2 for S. The numbers are right, but the order is reversed, and later steps inherit the error.
| Step | Wrong | Right |
|---|---|---|
| Order of S | 3 × 2 | 2 × 3 |
| Entry in row 2, column 1 of S | 5 | 8 |
| Why | Column counted first | Row first, then column |
Always say “rows first” aloud when you write the order. In multiplication, this same habit decides whether a product exists.
Check yourself
For the matrix below, state the order and find the entry in row 3, column 1.
P = | 5 2 |
| 7 −3 |
| 1 8 |Answer
P has 3 rows and 2 columns, so its order is 3 × 2.
Row 3 is (1, 8). Column 1 of that row is 1, so the entry is 1.
Check: the entry in row 1, column 2 is 2, not 5, because 5 is in column 1.
What to study next
Now that positions are clear, move to adding and multiplying matrices. You can test your own matrices with the two-by-two matrix operations tutor. Log any slips in the mistake log and paper-error review.
If you want a teacher to watch your working, see online one-to-one Mathematics tuition.