Matrices · Form 5
What is a matrix, and what is its order?
A matrix is a rectangular arrangement of numbers in rows and columns; its order is simply how many rows by how many columns it has.
A tidy box of numbers
A matrix is just numbers set out in a rectangle of rows and columns, held inside brackets. Each number in it is called an element.
Written this way, a whole table of data, prices, marks, quantities, becomes a single object you can add, subtract and multiply.
Reading the order: rows first, then columns
The order of a matrix is written rows × columns, always in that sequence. A matrix with 2 rows and 3 columns has order 2 × 3, no matter what the numbers inside are.
The order tells you the shape of the matrix at a glance, before you do anything with it.
Why the order is the first thing to check
Order decides what you are allowed to do: you can only add or subtract matrices that share the same order. The common slip is reading it the wrong way round, a 2 × 3 matrix is not the same as a 3 × 2 one, because rows always come before columns.
Get the order right first and the rest of the chapter falls into place.
Source:DSKP KSSM Mathematics Form 4 and 5 (Versi English)
Frequently asked questions
How do I state the order of a matrix correctly?
Count the number of rows first, then the number of columns, and write it as rows × columns. A matrix with 2 rows and 3 columns has order 2 × 3, not 3 × 2.
Always count rows before columns, the order is never written the other way round.
Why does a matrix's order matter for addition and multiplication?
For addition or subtraction, both matrices must have exactly the same order. For multiplication, the number of columns in the first matrix must equal the number of rows in the second, the product then takes the outer order, rows of the first by columns of the second.
What mistake do students make when stating a matrix's order?
The most common slip is swapping rows and columns, writing 3 × 2 for a matrix that actually has 3 columns and 2 rows. Another mistake is assuming any two matrices can be added just because they have the same number of elements, the arrangement into rows and columns must match too.