The Vandermonde matrix with nodes x1,x2,…,xnx_1, x_2, \ldots, x_nx1,x2,…,xn has the form V=(1x1x12⋯x1n−11x2x22⋯x2n−1⋮⋮⋮⋱⋮1xnxn2⋯xnn−1)V = \begin{pmatrix} 1 & x_1 & x_1^2 & \cdots & x_1^{n-1} \\ 1 & x_2 & x_2^2 & \cdots & x_2^{n-1} \\ \vdots & \vdots & \vdots & \ddots & \vdots \\ 1 & x_n & x_n^2 & \cdots & x_n^{n-1} \end{pmatrix}V=11⋮1x1x2⋮xnx12x22⋮xn2⋯⋯⋱⋯x1n−1x2n−1⋮xnn−1 with determinant det(V)=∏1≤i<j≤n(xj−xi)\det(V) = \prod_{1 \leq i < j \leq n} (x_j - x_i)det(V)=∏1≤i<j≤n(xj−xi). Compute det(V)\det(V)det(V) for nodes x1=1,x2=2,x3=4x_1 = 1, x_2 = 2, x_3 = 4x1=1,x2=2,x3=4.
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