FINLANDIA SCHOOLA matrix is a rectangular arrangement of numbers or mathematical expressions in rows and columns.
For example:
This matrix has:
2 rows
3 columns
Therefore, its order is:
Elements
The element in row 1, column 2 is:
The element in row 2, column 3 is:
8. Addition and Subtraction of Matrices
Matrices can only be added or subtracted when they have the same order.
Given:
and
Addition
Subtraction
9. Multiplication of Matrices
This is an important SS 3 examination skill.
A matrix � of order � can multiply matrix � of order �.
The inside numbers must be the same:
The resulting matrix has order:
Example
Then:
Therefore:
Important misconception
Matrix multiplication is generally not commutative.
That means:
in general.
10. Matrices as Linear Transformations
A matrix can transform the coordinates of a point.
For example, consider:
and the point:
Then:
Therefore:
The matrix has enlarged the coordinates by scale factor 2.
Other transformations
Students should recognise matrices representing transformations such as:
Enlargement
Reflection
Rotation
Stretching
For example, reflection in the �-axis can be represented by:
11. Determinants
For a � matrix:
the determinant is:
Example
Therefore:
Memory aid
Multiply the main diagonal, subtract the other diagonal.
12. Determinant of a � Matrix
For:
the determinant can be calculated by expansion along a row or column.
For example:
Expanding along the first row:
13. Solving Simultaneous Equations Using a � Matrix
Consider:
Write in matrix form:
This can be written as:
Therefore:
For:
For this example:
Hence:
Multiplying by:
gives:
14. Solving � Simultaneous Equations
For three equations:
write:
where:
and:
Then, where � exists: