Practice question · True or false
3×3 matrices are sufficient for 3D graphics; the 4×4 convention exists only for historical reasons.
Hints
- Can a 3×3 matrix move the origin?
- Translation is not a linear map.
Show the answer
False
Why
False. A 3×3 matrix always fixes the origin, so it cannot express translation. Homogeneous coordinates add a fourth component precisely so that translation becomes a matrix multiply and the whole transform chain — rotate, scale, translate, project — composes into a single 4×4 product.
Practise Linear Transformations
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More questions on Linear Transformations
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