A matrix of the form
is called a Vandermonde matrix.14
a) Show that if n = 2,
det(V) = x2 – x1.
b) Use row operations to show that if n = 3, det(V) = (x2 – x1)(x3 – x1)(x3 – x2).
c) Use row operations to show that if n = 4, det(V) = (x2 – x1) (x3 – x1)(x4 – x1)(x3 – x2)(x4 – x2)(x4 – x3).
d) In general,
Prove this result.
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