Practice question · Multiple choice
Rotating a 3D model by 90° about x then 90° about y gives a different orientation than doing them in the reverse order. Which algebraic fact is that?
Hints
- Try it with a book. Rotate about one axis then the other, then swap the order.
- Ask which algebraic property would have to hold for the two results to match.
Show the answer
D. Non-commutativity of matrix multiplication, since AB ≠ BA
Why
Composition is matrix multiplication and matrices do not commute, so order is physically visible on a book in your hands. It is why 3D rotation order must be specified, XYZ or ZYX are different conventions, and why quaternions are preferred, since interpolating Euler angles hits gimbal lock.
Practise Linear Transformations
The app has 4 more questions on this lesson, and keeps your place in the course. Computer Science I is free to start.
More questions on Linear Transformations
- Order the steps to find the matrix of a linear transformation T on the plane.
- Select every transformation of the plane that is linear.
- Rotation and scaling are linear transformations of the plane; translation is not. Why does moving every point…
- 3×3 matrices are sufficient for 3D graphics; the 4×4 convention exists only for historical reasons.