Practice question · Multiple choice
Every linear transformation sends the origin to the origin. Why does that rule out translation, which seems the simplest transformation of all?
Hints
- Apply to the zero vector.
- Ask why computer graphics uses 4×4 matrices for 3D.
Show the answer
A. Because linearity requires and translation moves it
Why
Translation fails the definition at a single point, the origin. Homogeneous coordinates embed the plane in 3D so that a shear there projects down to a translation here.
Practise Linear Transformations
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