O-Level E-Math and SEC G3 Mathematics K310
N9: Matrices
Use matrix notation and operations only within the current K310 scope, with dimensions checked before calculation.
Core notes
Matrices organise data and transformations by rows and columns. State the order, interpret the labels, and check dimensional compatibility before performing an operation.
Displaying and interpreting data
An matrix has rows and columns. Its entries have meaning only through the supplied row and column labels, so identify both before reading a value.
Scalar multiplication
Multiplying a matrix by a scalar multiplies every entry and leaves the order unchanged. In context, the scalar may represent a unit price, conversion factor or repeated quantity.
Matrix sums and products
Matrices of equal order add entry by entry. For , combine each row of with each column of ; the product has the outer dimensions. Matrix multiplication is not generally commutative.
Formulae and methods
| Relationship | Use |
|---|---|
| Check matrix-product dimensions. |
Worked examples
Example 1: A bundle contains pens and files. Pens cost and files cost . Use a matrix product to find the cost.
- Use quantity row matrix .
- Use price column matrix .
- Calculate .
Answer: The bundle costs .
Example 2: Given , find .
- Keep the order.
- Multiply each entry by .
- Write the four resulting entries in their original positions.
Answer: .
Chapter checkpoint
- State the matrix order as rows by columns.
- Add only matrices with the same order and multiply only when inner dimensions match.
- Interpret the resulting entries using the original row and column labels.
Exam traps and retrieval check
Avoid these traps
- Multiplying entries position by position instead of row by column.
- Assuming .
- Reporting a matrix without interpreting its labels or units.
Check from memory
What is the order of a matrix with rows and columns?
.
When can two matrices be added?
When they have the same order.
What determines whether exists?
The number of columns of must equal the number of rows of .
Official K310 coverage
This chapter maps to 4 official outcomes: N9.1, N9.2, N9.3, N9.4. Check the official 2027 K310 syllabus for exact assessable wording and paper details.