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The question: Evaluate $$\sum_{k=0}^4 c_kx^k$$ for $x=0,1,2,3,4$. Write these five expressions as a matrix product $Mc$, where $M$ is a 5x5 matrix, and $c$ is a column matrix with components $c_0,c_1,....,c_4$.

Would I just plug in the different $x$ values for this? We're covering uniform B-splines, but I don't see how this has anything to do with it.

Any input is appreciated, thanks.

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This problem does not directly involve B-splines, but it teaches you background knowledge you need in order to understand B-splines. – littleO Nov 5 '12 at 8:27
up vote 1 down vote accepted

The matrix $M$ is \begin{equation} M = \begin{bmatrix} 1 & x_0 & x_0^2 & x_0^3 & x_0^4 \\ 1 & x_1 & x_1^2 & x_1^3 & x_1^4 \\ 1 & x_2 & x_2^2 & x_2^3 & x_2^4 \\ 1 & x_3 & x_3^2 & x_3^3 & x_3^4 \\ 1 & x_4 & x_4^2 & x_4^3 & x_4^4 \end{bmatrix} \end{equation} where $x_k = k$ for $k = 0,1,2,3,4$.

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