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You may vary the matrix by adjusting the sliders at the top and you may vary the region to be transformed by moving the points of the square on the left. You will see the effects of the transformation on the right.
What is the connection between the determinant of the matrix and the area scale factor of the transformation?

Summary/Background

The determinant of the matrix gives the scale factor of the transformation.

Downloadable Files

Sketchpad - transf01Sketchpad - transf01
Investigate transformations further using Geometer's Sketchpad

Software/Applets used on this page

David Austin
Java applet from David Austin

Glossary

matrix

a rectangular or square grid of numbers.

transformation

A change in form or shape.

Full Glossary List

This question appears in the following syllabi:

SyllabusModuleSectionTopicExam Year
AQA A-Level (UK - Pre-2017)FP1Matrix algebraTransformation geometry-
AQA AS Further Maths 2017Pure MathsMatrices and TransformationsLinear Transformations-
AQA AS/A2 Further Maths 2017Pure MathsMatrices and TransformationsLinear Transformations-
CCEA A-Level (NI)FP1Matrix algebraTransformation geometry-
Edexcel A-Level (UK - Pre-2017)FP1Matrix algebraTransformation geometry-
Edexcel AS Further Maths 2017Core Pure MathsLinear TransformationsLinear Transformations-
Edexcel AS/A2 Further Maths 2017Core Pure MathsLinear TransformationsLinear Transformations-
Methods (UK)M5Matrix algebraTransformation geometry-
OCR A-Level (UK - Pre-2017)FP1Matrix algebraTransformation geometry-
OCR AS Further Maths 2017Pure CoreLinear TransformationsLinear Transformations-
OCR MEI AS Further Maths 2017Core Pure ALinear TransformationsLinear Transformations-
OCR-MEI A-Level (UK - Pre-2017)FP1Matrix algebraTransformation geometry-
Scottish Advanced HighersM3Matrix algebraTransformation geometry-
Scottish (Highers + Advanced)AM3Matrix algebraTransformation geometry-
Universal (all site questions)MMatrix algebraTransformation geometry-
WJEC A-Level (Wales)FP1Matrix algebraTransformation geometry-