Hey there! Sign in to join this conversationNew here? Join for free
    • Thread Starter

    hello i have two questions infont of me that i dont no how to start or even do, they are as followed...

    Let A = (4 2)
    (-3 -1)
    (A)Find an invertible matrix P such that P^-1AP is diagonal, compute P^-1.

    (B) Find scalars U1 and U2 such that A^6=U1A^5 + U2A^4

    Thanks for your help!

    Let D be the diagonal matrix such that D=P^{-1}AP.

    Then D contains the eigenvalues of A along its diagonal, and P has the corresponding eigenvectors as its columns.

    D=P^{-1}AP <=> A=PDP^{-1}

    Then note that A^n=(PDP^{-1})^n=PD(P^{-1}P)D(P^{-1}P)D....DP^{-1}=PD^nP^{-1}. (as P^{-1}P=I)

    From there it should be inspection.
Do you agree with the PM's proposal to cut tuition fees for some courses?
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.