1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

  1. Feb 24, 2009 #1
    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 |

    = [tex]\prod [/tex] (aj - ai)

    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 =
    = [tex]\Pi [/tex]0<i<j<n (aj - ai) [tex]\Pi [/tex]0<k<n (an - ak)
    Last edited: Feb 24, 2009
  2. jcsd
  3. Feb 25, 2009 #2


    User Avatar
    Science Advisor
    Homework Helper

    Hi rosh300! :smile:

    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.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook