Practice question · True or false
Because is a basis for polynomials of degree at most 2, every such polynomial has exactly one expression in terms of it.
Hints
- What does a basis guarantee beyond spanning?
- Independence forces the coefficients to be unique.
Show the answer
True
Why
True. Spanning gives at least one expression; independence gives at most one, and together exactly one. That uniqueness is what makes coordinates meaningful, it is why can be identified with the triple and why the space is 3-dimensional.
Practise Basis and Dimension
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