Practice question · Put in order
Order the steps to test whether two plane vectors u and v are linearly independent.
- Conclude they are independent and form a basis for the plane
- If yes, they are dependent
- Ask whether one vector is a scalar multiple of the other
- If no, they point in genuinely different directions
Hints
- For just two vectors, independence reduces to a single check.
- Two non-parallel vectors in R^2 automatically span it.
Show the answer
- Ask whether one vector is a scalar multiple of the other
- If yes, they are dependent
- If no, they point in genuinely different directions
- Conclude they are independent and form a basis for the plane
Why
For two vectors, independence is exactly 'neither is a multiple of the other'. Two independent vectors in R^2 also span the plane, so they form a basis.
Practise Linear Independence and Basis
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 Independence and Basis
- A model trained on 50 features has coefficients that swing wildly between refits while its predictions stay…
- A dataset with 50 correlated features can be well approximated using far fewer dimensions.
- In the plane R^2, sort each set of vectors by what it does.
- Select every set of vectors that forms a BASIS for the plane R^2.