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

    21
    ReputationRep:
    (Original post by B_9710)
    You just have to know which trig functions are positive and negative in a given interval. Like you just know that for  0\leq x <\pi /2 ,\ \cos x is positive and for  \pi /2 < x \leq  \pi, \ \cos x is negative.
    Damn it was so easy haha, thank you!
    Spoiler:
    Show
    You can probably tell I haven't done much maths this summer.
    Offline

    1
    ReputationRep:
    how can three equations of x+y+z = 0 formed from a matrix give an eigenvector of (p, q, -p-q)?

    Thanks
    • Community Assistant
    • Welcome Squad
    Offline

    20
    ReputationRep:
    Community Assistant
    Welcome Squad
    (Original post by Daiblain)
    how can three equations of x+y+z = 0 formed from a matrix give an eigenvector of (p, q, -p-q)?

    Thanks
    Sorry, I either don't understand the question, or I don't think you gave enough information there. I think it's the latter.
    Offline

    15
    ReputationRep:
    (Original post by Daiblain)
    how can three equations of x+y+z = 0 formed from a matrix give an eigenvector of (p, q, -p-q)?

    Thanks
    Well all three equations agree if  x=p,  y=q then  p+q+z=0 so of course  z=-p-q .
    Do you notice that there are many solutions you can try, say  \begin{pmatrix} \alpha \\ -\alpha \\ 0 \end{pmatrix} or  \begin{pmatrix} \beta \\ \beta \\ -2\beta \end{pmatrix} . You actually get an eigenplane, and the eigenplane has equation  x+y+z=0 and you can parametrise the plane in anyway you want if you want it in parametric form. All you would do is add any two linearly independent eigenvectors to get it in parametric form.
    Offline

    1
    ReputationRep:
    (Original post by RDKGames)
    Sorry, I either don't understand the question, or I don't think you gave enough information there. I think it's the latter.
    (Original post by B_9710)
    Well all three equations agree if  x=p,  y=q then  p+q+z=0 so of course  z=-p-q .
    Do you notice that there are many solutions you can try, say  \begin{pmatrix} \alpha \\ -\alpha \\ 0 \end{pmatrix} or  \begin{pmatrix} \beta \\ \beta \\ -2\beta \end{pmatrix} . You actually get an eigenplane, and the eigenplane has equation  x+y+z=0 and you can parametrise the plane in anyway you want if you want it in parametric form. All you would do is add any two linearly independent eigenvectors to get it in parametric form.
    Sorry, It's my fault Matrix with eigenvalue 5 is (-211)(1-21)(11-2) to give -2x+y+z = 0, x-2y+z =0 and x+y-2z=0I eliminated one variable to make x=y=z because I can't really see it off the bat, making the eigenvector (x,x,x) -> x(1,1,1)With eigenvalue 2 you get(111)(111)(111)to give x+y+z=0all of this was taken off the mei fp2 book, i just didnt understand the eigenvector that goes with the last matrixThanks a bunch!
    Offline

    1
    ReputationRep:
    Yeah, the post came out great
    • Thread Starter
    Offline

    12
    ReputationRep:
    Term hasn't even started and yet the thread already has 10% of the posts that the Year 12 thread had.

    Speaking of the Year 12 thread, time for me to bump it!
    • Thread Starter
    Offline

    12
    ReputationRep:
    Are all summations of the form \sum^{\infty}_{r=1} \frac{1}{ar+b} where a,b \in \mathbb{R} divergent?
    Offline

    10
    ReputationRep:
    (Original post by Palette)
    Are all 'things' of the form \sum^{\infty}_{r=1} \frac{1}{ar+b} where a,b \in \mathbb{R} divergent?
    Yes - take out a factor of (1/a) and you get the sum from 1 to infinity of (1/(x+(b/a)) - which is just a shift of the sum of 1/x - which with these limits we know diverges
    (and in the case a=0 you just have an infinite number of '1/b's added together which must diverge)
    • Thread Starter
    Offline

    12
    ReputationRep:
    (Original post by ValerieKR)
    Yes - take out a factor of (1/a) and you get the sum from 1 to infinity of (1/(x+(b/a)) - which is just a shift of the sum of 1/x - which we know diverges
    (and in the case a=0 you just have an infinite number of '1/b's added together which must diverge)
    Thanks for the help; do you mind if I add your name to the helpers list?
    Offline

    10
    ReputationRep:
    (Original post by Palette)
    Thanks for the help; would you mind if I add your name to the helpers list?
    What responsibility does being one involve?
    • Thread Starter
    Offline

    12
    ReputationRep:
    (Original post by ValerieKR)
    What responsibility does being one involve?
    Nothing more than what you're currently doing.
    Offline

    10
    ReputationRep:
    (Original post by Palette)
    Nothing more than what you're currently doing.
    Ok - sure
    Offline

    5
    ReputationRep:
    How do u integrate 1/x^2+1
    Offline

    15
    ReputationRep:
    (Original post by youreanutter)
    How do u integrate 1/x^2+1
    Use sub  x=\tan \theta .
    Offline

    5
    ReputationRep:
    (Original post by B_9710)
    Use sub  x=\tan \theta .
    Is that a c4 method?
    Offline

    15
    ReputationRep:
    (Original post by youreanutter)
    Is that a c4 method?
    This integral is not expected is C4 but you can still apply normal substitution methods.
    Offline

    21
    ReputationRep:
    Do we need to remember the harmonic identities? Or do we get given them in the question?
    • Very Important Poster
    Offline

    21
    ReputationRep:
    Very Important Poster
    (Original post by jamestg)
    Do we need to remember the harmonic identities? Or do we get given them in the question?
    http://www.mathsnetalevel.com/downlo...ook.pdf#page=8
    Offline

    21
    ReputationRep:
    Thanks! I'm sure I printed off this haha, probably stored it away with all my AS work...

    Looks like I'm going to have to get revising
 
 
 
  • 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
    Would you rather give up salt or pepper?
    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

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