Inverse Matrix Transformations (Edexcel International A Level (IAL) Further Maths): Revision Note
Exam code: YFM01
Inverse Matrix Transformations
What are inverse matrix transformations?
If the matrix
transforms the point P to P’ then
the inverse matrix
transforms P’ back to P
Inverse matrices represent the reverse of the transformation
Applying a transformation then its inverse returns points to their original positions
How do I use inverse matrix transformations?
You can often interpret inverse matrix transformations geometrically
For example, let
represent a rotation of 90° clockwise
Then
must represent a rotation of 90° anticlockwise
is also the same as a rotation of 270° clockwise (
)
So
giving
This says four rotations of 90° clockwise returns to the original position
If
then the inverse does the same thing as the transformation
For example. the reverse of reflecting in the y-axis is reflecting in the y-axis!
also gives
This says reflecting twice about the y-axis returns to the original position
Worked Example
The matrix represents a rotation of 120° anticlockwise about the origin.
(a) Describe fully the single transformation represented by .
The inverse of reverses the transformation
represents a rotation of 120° clockwise about the origin
(b) Use a geometrical argument to explain why .
means apply the transformation represented by
twice
represents a rotation of 240° anticlockwise about the origin
Rotating 240° anticlockwise is the same as rotating 120° clockwise
A rotation of 120° clockwise about the origin, , is the same as doing a rotation of 240° anticlockwise about the origin,
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