I'm learning about Vandermonde matrix to get monomial basis.
Suppose I have 4 points $(-1, 2),~ (0,7),~ (1,22) $ and $ (2,71)$
I was taught how to create the Vandermonde matrix using arbitrary numbers: $$\begin{bmatrix}1 &&x^1&& x^2 &&x^3&&\dots&& x^n\\ 1 &&y^1&& y^2 &&y^3 &&\dots&&y^n\\ 1&& z^1&& z^2&& z^3 &&\dots&&z^n\\ 1&& r^1&& r^2&& r^3&&\dots&& r^n\end{bmatrix}$$
where n = number of points - 1. I'm not sure if I was taught this correctly.
Is this the Vandermonde matrix, given the points: $$\begin{bmatrix}1&& 1&& -1&& 1\\ 1 &&0 &&0 &&0\\ 1 &&1 && 1 &&1\\ 1&& 2&& 4 &&8\end{bmatrix}$$