Practice question · Multiple choice
A pilot flies 100 km north then 100 km east, and a second flies 100 km east then 100 km north. They land in the same place. Why does vector addition commute when matrix multiplication does not?
Hints
- Draw both routes as a parallelogram. Where is the corner?
- Now rotate a book then flip it, and flip then rotate. Compare.
Show the answer
B. Because addition combines displacements while matrices compose actions
Why
Displacements add up to the same corner whichever leg you walk first. A matrix does something to space, and rotate-then-reflect is a different operation from reflect-then-rotate, which is why the same subject has one commutative operation and one that is not, and the difference is quantity against action.
Practise Vectors in the Plane and Space
The app has 6 more questions on this lesson, and keeps your place in the course. Mathematics I is free to start.