Turn on thread page Beta
    • Thread Starter


    hi, basically i don't know where the [1, 0, 0] matrix came from, or where they got the following two matrices for multiplication. i understand how they went on from there but i'm just not getting the whole (A-x1I)(A-x2I) equation? any help? thank you!

    For a general matrix A, suppose the eigenvectors are v1, v2, v3.

    Then we know (1, 0, 0) can be written as a1v1+a2v2+a3v3 for some scalars v1, v2, v3.

    Then multiplying by (A-x1I) "kills off" the a1v1 component (since A-x1I)v1 = 0.
    Extending this idea, multiplying by (A-x1I)(A-x2I) kills off the a1v1 and a2v2 components, leaving only a multiply of v3, the third eigenvector.

    [Note that there are various (uncommon) situations where this approach fails, either because v3 has the same eigenvalue as one of v1, v2 (in which case (A-x1I)(A-x2I) kills off v3 as well), or because the representation of (1, 0, 0) in terms of v1, v2, v3 has a3v3 = 0].
The home of Results and Clearing


people online now


students helped last year

University open days

  1. Sheffield Hallam University
    City Campus Undergraduate
    Tue, 21 Aug '18
  2. Bournemouth University
    Clearing Open Day Undergraduate
    Wed, 22 Aug '18
  3. University of Buckingham
    Postgraduate Open Evening Postgraduate
    Thu, 23 Aug '18
A-level students - how do you feel about your results?
Useful resources

Make your revision easier


Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here


How to use LaTex

Writing equations the easy way

Student revising

Study habits of A* students

Top tips from students who have already aced their exams

Study Planner

Create your own Study Planner

Never miss a deadline again

Polling station sign

Thinking about a maths degree?

Chat with other maths applicants

Can you help? Study help unanswered threads

Groups associated with this forum:

View associated groups

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

Write a reply...
Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.