$(3, 2)$ is the coordinate vector of $3 + 2x$, relative to the basis $(1, x)$
Terms
| Term | This example | Why |
|---|---|---|
| coordinate vector | ✓ | $3 + 2x$ is the linear combination of the basis vectors using the coefficients $3$ and $2$: \(3 + 2x = 3(1) + 2(x)\) |
Distinctions using this example
- Vector vs. coordinate vector: $(3, 2)$ is the coordinate vector of $p = 3 + 2x$ relative to the basis $(1, x)$, because $p = 3 \cdot 1 + 2 \cdot x$.