# Vandermondegive an example of determinant Vandermonde

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### 1 Answer

We'll write the form of a Vandermonde determinant:

|1 1 1|

det A = |a b c|

|a^2 b^2 c^2|

We notice that the terms of each column are the terms of a geometric progression.

We'll take the 1st column:

1 a a^2 = a^0 a^1 a^2

The common ration of the geometric progresion is a.

We'll take the 2nd column:

1 b b^2 = b^0 b^1 b^2

The common ration of the geometric progresion is b.

We'll take the 1st column:

1 c c^2 = c^0 c^1 c^2

The common ration of the geometric progresion is c.

The value of Vandermonde determinant is the product of differences between a,b,c.

det A = (b-a)(c-a)(c-b)

A Vandermonde determinant could also have the terms of the lines as being the terms of a geometric progression.