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

    8
    ReputationRep:
    Attachment 700320
    Stuck on a problem, don't really know how to go about it or what sort of answers it is actually looking for... I got the augmented matrix into RREF and unsure where to go from here. I'm guessing part (a) is when t is any real number except -2. Any advice would be appreciated :-)
    Offline

    10
    ReputationRep:
    (Original post by youngar)
    Attachment 700320

    Stuck on a problem, don't really know how to go about it or what sort of answers it is actually looking for... I got the augmented matrix into RREF and unsure where to go from here. I'm guessing part (a) is when t is any real number except -2. Any advice would be appreciated :-)
    For some reason, I can not see the image/question.
    • Thread Starter
    Offline

    8
    ReputationRep:
    (Original post by simon0)
    For some reason, I can not see the image/question.
    Is that any better?
    Attached Images
     
    • Community Assistant
    • Welcome Squad
    Offline

    20
    ReputationRep:
    (Original post by youngar)
    Is that any better?
    You get a no/infinite solutions when the determinant of that matrix equals 0. What's the determinant of that in terms of t? Hence what values of t make it zero? Then the answer to part (A) is t \in \mathbb{R} \setminus \{t_1, t_2\} for whatever t_1,t_2 you find as your answers here.

    Then you need to consider what happens to your RREF when t=t_1,t_2 hence deduce which one gives infinite sols and which one gives no sols.

    Also, if that RREF correct...?
    • Thread Starter
    Offline

    8
    ReputationRep:
    (Original post by RDKGames)
    You get a no/infinite solutions when the determinant of that matrix equals 0. What's the determinant of that in terms of t? Hence what values of t make it zero? Then the answer to part (A) is t \in \mathbb{R} \setminus \{t_1, t_2\} for whatever t_1,t_2 you find as your answers here.

    Then you need to consider what happens to your RREF when t=t_1,t_2 hence deduce which one gives infinite sols and which one gives no sols.

    Also, if that RREF correct...?
    I've tried it again a few times and that's what I keep getting. Though I'm guessing it is incorrect as you can't get the determinant in terms of t...
    • Community Assistant
    • Welcome Squad
    Offline

    20
    ReputationRep:
    (Original post by youngar)
    I've tried it again a few times and that's what I keep getting. Though I'm guessing it is incorrect as you can't get the determinant in terms of t...
    Huh...?

    Well the determinant in terms of t is just \begin{vmatrix} t & 1 & 1 \\ 1 & t & 1 \\ 1 & 1 & t \end{vmatrix}=t[t^2-1]-[t-1]+[1-t] which can be factorised fully to give two values of t for which the system has no unique sols - your RREF does not completely reflect on that, AFAIK.
    • Thread Starter
    Offline

    8
    ReputationRep:
    (Original post by RDKGames)
    Huh...?

    Well the determinant in terms of t is just \begin{vmatrix} t & 1 & 1 \\ 1 & t & 1 \\ 1 & 1 & t \end{vmatrix}=t[t^2-1]-[t-1]+[1-t] which can be factorised fully to give two values of t for which the system has no unique sols - your RREF does not completely reflect on that, AFAIK.
    Ohhhh I must be lost off somewhere here cause I thought it was the determinant of the RREF matrix (which is only actually gonna be 1 loool) my bad. Let me give it another go and I might get back to you if needs be.

    Thanks.
    • Thread Starter
    Offline

    8
    ReputationRep:
    RDKGames

    Name:  hw3 q4.png
Views: 9
Size:  180.9 KB

    Sorry to be a pain but just wondering how this looks? Supposed to be using the RREF to solve these but thought I'd figure it this way first so I know if I'm heading in the right direction or not.
    Offline

    17
    ReputationRep:
    No-one ever listens to me on this, but if you have a question like this and it asks you for actual solutions, you might as well simply try to solve the equations (use echelon form etc if you wish), being careful to take note of any places where you might want to divide by 0.

    Because yes, there's a nice swish method of using the determinant to find when you don't get a unique solution, but this doesn't actually help you with finding the solutions, so what's the point, really?
    Offline

    10
    ReputationRep:
    (Original post by youngar)
    RDKGames

    Name:  hw3 q4.png
Views: 9
Size:  180.9 KB

    Sorry to be a pain but just wondering how this looks? Supposed to be using the RREF to solve these but thought I'd figure it this way first so I know if I'm heading in the right direction or not.
    Looks fine except for the case of where unique solutions exists where:

     \underline{x} = \begin{pmatrix} 1/(t-1) \\ 1/(t-1) \\ 1/(t-1) \end{pmatrix}.

    As for the random case of t=2:

     \begin{pmatrix} t & 1 & 1 \\ 1 & t & 1 \\ 1 & 1 & t \end{pmatrix} \begin{pmatrix} 1/(t-1) \\ 1/(t-1) \\ 1/(t-1) \end{pmatrix}  ,

     = \begin{pmatrix} 2 & 1 & 1 \\ 1 & 2 & 1 \\ 1 & 1 & 2 \end{pmatrix} \begin{pmatrix} 1 \\ 1 \\ 1 \end{pmatrix} \, = \, \begin{pmatrix} 4 \\ 4 \\ 4 \end{pmatrix} \, \neq \, \begin{pmatrix} 1 \\ 1 \\ 1 \end{pmatrix}.

    Note you have the matrix in Hermtie form where the solutions could be read off.
 
 
 
  • 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
    Did TEF Bronze Award affect your UCAS choices?
    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.