To prove that the determinant of the Vandermonde matrix V is
Explanation of Solution
Given information:
Vandermonde matrix V is given by
Explanation:
Start with induction on n .
For n = 1, the Vandermonde matrix is of size
Now, assume that the given condition is true for
Start from second last column on right side that is
The determinant will not be changed from this operation. All entries in the top row, except the leftmost one, have become zero as
After taking factors out,a
Thus, this completes the induction.
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