Vandermonde Matrix - Solving a 3x3 Determinant Question

  • Thread starter Thread starter obiwan
  • Start date Start date
  • Tags Tags
    Matrix
Click For Summary
SUMMARY

The discussion focuses on solving a 3x3 Vandermonde Matrix determinant, specifically demonstrating that the determinant of the matrix formed by the rows [1, 1, 1], [x, y, z], and [x², y², z²] equals (x-y)(y-z)(z-x). The user initially struggled with the concept but successfully utilized a formula found on Wikipedia to arrive at the solution. This highlights the importance of understanding the properties of Vandermonde matrices in linear algebra.

PREREQUISITES
  • Understanding of determinants in linear algebra
  • Familiarity with Vandermonde matrices
  • Basic knowledge of polynomial functions
  • Experience with matrix operations
NEXT STEPS
  • Study the properties of Vandermonde matrices in detail
  • Learn how to compute determinants of larger matrices
  • Explore applications of Vandermonde determinants in polynomial interpolation
  • Review linear algebra concepts related to matrix theory
USEFUL FOR

Students studying linear algebra, mathematicians interested in matrix theory, and anyone looking to deepen their understanding of determinants and their applications.

obiwan
Messages
2
Reaction score
0
[SOLVED] Vandermonde Matrix - Help!

Hi everyone, I am new to the forum.

I'm bit confused in a particular 3by3 Vandermonde Matrix question and really appreciate if someone can help me with it.

Homework Statement

The question states 'Show that the 3 by 3 Vandermonde Determinant:
1 1 1
det x y z = (x-y) (y-z) (z-x)
x^2 y^2 z^2

I have not made an attemt to the question as I haven't got a clue.

Your help and time are much appreciated. thanksPS. Just realized the rows are not aligned under one another but It is a 3by3 Matrix with the first rows 1, 1, 1 second Row x, y, z and the third row x^2, y^2, z^2.
 
Last edited:
Physics news on Phys.org
Well, how do you take the determinant of a 3x3 matrix?
 
Thanks Cristo. I've managed to show the determinant using a simple formula I came across on wikipedia. Thanks for your help anyway.
 

Similar threads

Decompose 4x4 determinant into 24 determinants -- How many are zero?
  • · Replies 1 ·
Replies
1
Views
2K
Prove the identity matrix is unique
  • · Replies 69 ·
3
Replies
69
Views
11K
Solving a System of Equations via the Matrix Method
  • · Replies 9 ·
Replies
9
Views
3K
How many birds of each kind did I buy?
  • · Replies 5 ·
Replies
5
Views
2K
Finding argument of complex number
  • · Replies 10 ·
Replies
10
Views
2K
Find inverse matrix using determinants and adjoints
  • · Replies 7 ·
Replies
7
Views
2K
Undergrad Convention for writing $\binom{1}{1}$ tensors in matrix form?
  • · Replies 8 ·
Replies
8
Views
2K
The infinite limits of the probability transition matrix for Markov chain
  • · Replies 24 ·
Replies
24
Views
4K
How Do You Solve Systems of Linear Equations with Parameters?
  • · Replies 2 ·
Replies
2
Views
2K
Python Partial pivoting in getting the reduced row echelon form of a matrix
  • · Replies 2 ·
Replies
2
Views
2K