Practice question · Select all that apply
Select every set that the lesson presents as a vector space under its natural addition and scaling.
Hints
- A set qualifies when its members can be added and scaled and the axioms still hold; the members need not look like arrows.
- Test the fourth option: add two vectors of length 1 together and ask whether the result is still in the set.
Show the answer
- A. Functions
- B. Arrows in the plane
- C. Matrices
- E. Polynomials
Why
Arrows, polynomials, matrices and functions can all be added and scaled, so all four are vector spaces, that generality is the point of the abstraction. The unit vectors are not: (1, 0) + (0, 1) has norm about 1.41, so the sum leaves the set, and scaling by 2 leaves it too.
Practise Vectors and Vector Spaces
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