Homework Help: Proving a formula for the determiante in a special matrix

1. Feb 24, 2009

rosh300

1. The problem statement, all variables and given/known data

Let a1, a2 are real numbers, where n > 1 show that: determinant of:

| 1 a1 a21 .... .... an-11 |
| 1 a2 a22 .... .... an-12 |
:
:
| 1 an a2n .... .... an-1n |

= $$\prod$$ (aj - ai)
1$$\leq$$i<j<n

2. Relevant equations
if you row reduce a matrix the determinate is the product of the leading diagonal(previous question was finding determinate of matrices by row reducing them)

3. The attempt at a solution
tried using induction but get stuck very quickly.
i got RHS =
= $$\Pi$$0<i<j<n (aj - ai) $$\Pi$$0<k<n (an - ak)

Last edited: Feb 24, 2009
2. Feb 25, 2009

tiny-tim

Hi rosh300!

But that's the answer, isn't it?

The first part is all non-identical pairs up to n-1, and the second part is all non-identical pairs of which the higher is n.