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

    13
    ReputationRep:
    Name:  Matrices.png
Views: 10
Size:  7.5 KB
    • Community Assistant
    • Welcome Squad
    Online

    20
    ReputationRep:
    (Original post by F3rnw3h)
    Name:  Matrices.png
Views: 10
Size:  7.5 KB
    Are you struggling? Posting for fun?

    If you're stuck on it, post your attempt.
    • Thread Starter
    Offline

    13
    ReputationRep:
    Name:  Matrices.png
Views: 5
Size:  7.5 KB
    I first used the equation 'Ms=λs,
    and found the eigenvalue to be -1, and k to be -12,

    I then used the equation det(M-λI)=0 using Sarrus' method giving me:

    16(8-λ) - 30(-3-λ) - 24(-3-λ)
    = 38 λ + 290 (multiplying right to left)

    (-3-λ)(8-λ)(-3-λ) + 96 + 120
    = -λ^3 + 2λ^2 + 39λ + 72 (multiplying left to right)



    Giving the characteristic equation:

    = -λ^3 + 2λ^2 + λ - 263

    However, substituting λ=-1 into this equation does not give me zero :/
    I'm not sure where I've gone wrong?

    Thanks for any help!
    • Thread Starter
    Offline

    13
    ReputationRep:
    (Original post by RDKGames)
    Are you struggling? Posting for fun?

    If you're stuck on it, post your attempt.
    Ah sorry - accidentally pressed enter and it submitted before I wrote anything xD
    I've just reposted it -
    https://www.thestudentroom.co.uk/sho....php?t=5016162
    • Community Assistant
    • Welcome Squad
    Online

    20
    ReputationRep:
    (Original post by F3rnw3h)
    I first used the equation 'Ms=λs,
    and found the eigenvalue to be -1, and k to be -12,

    I then used the equation det(M-λI)=0 using Sarrus' method giving me:

    16(8-λ) - 30(-3-λ) - 24(-3-λ)
    = 38 λ + 290 (multiplying right to left)

    (-3-λ)(8-λ)(-3-λ) + 96 + 120
    = -λ^3 + 2λ^2 + λ - 263 (multiplying left to right)

    However, substituting λ=-1 into this equation does not give me zero :/
    I'm not sure where I've gone wrong?

    Thanks for any help!
    Not sure about this Sarrus' method, but that equation in \lambda seems to be incorrect.
    • Thread Starter
    Offline

    13
    ReputationRep:
    (Original post by RDKGames)
    Not sure about this Sarrus' method, but that equation in \lambda seems to be incorrect.
    I've multiplied it out again and still seem to get the same characteristic equation, so not sure where I've gone wrong
    Offline

    18
    ReputationRep:
    (Original post by F3rnw3h)
    I've multiplied it out again and still seem to get the same characteristic equation, so not sure where I've gone wrong
    I just did it with the Rule of Sarrus and got the correct answer. Check your signs, it should be (-3-\lambda)(8-\lambda)(-3-\lambda) + 120 + 96 - 16(8-\lambda) + 30(-3-\lambda) + 24(-3-\lambda)
    • Thread Starter
    Offline

    13
    ReputationRep:
    (Original post by _gcx)
    I just did it with the Rule of Sarrus and got the correct answer. Check your signs, it should be (-3-\lambda)(8-\lambda)(-3-\lambda) + 120 + 96 - 16(8-\lambda) + 30(-3-\lambda) + 24(-3-\lambda)
    Thanks! But I left them as positives and then subtracted that from my multiplication left to right, so it should give the same answer
 
 
 
  • See more of what you like on The Student Room

    You can personalise what you see on TSR. Tell us a little about yourself to get started.

  • Poll
    Will you be richer or poorer than your parents?
    Useful resources

    Make your revision easier

    Maths

    Maths Forum posting guidelines

    Not sure where to post? Read the updated guidelines here

    Equations

    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
  • See more of what you like on The Student Room

    You can personalise what you see on TSR. Tell us a little about yourself to get started.

  • 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

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