Vandermondegive an example of determinant Vandermonde

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giorgiana1976 | College Teacher | (Level 3) Valedictorian

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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.

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