1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Simple matrix/linear algebra question, help

  1. Apr 28, 2015 #1
    1. The problem statement, all variables and given/known data
    Here is the question, i know how to do part (i) but I do not understand part (ii):

    matrixq.png

    3. The attempt at a solution


    here's the solution from the marking scheme:

    matrixqans.png


    i understand how they formed the matrix from their working out (i can se the pattern), but I do not understand the actual working out. Thanks to anyone who could explain it to me.

    why does L(1) = t? why does L(t) = 1 + (-2)t? etc
     
  2. jcsd
  3. Apr 28, 2015 #2

    Mark44

    Staff: Mentor

    If f is a function in P3, then L(f) = f' + t * f(-2). In other words, to get the image of a function f, add the derivative of the function and t times f(-2). So L(1) = 0 + t = t. Can you figure out why L(t) = 1 - 2t?
     
  4. Apr 28, 2015 #3
    Still doesn't make sense.

    L(1) = 1' + 1*(-2)t = d(1)/dt + (-2)t =

    0 + (-2)t = (-2)t

    =/= t.



    what is f(-2) equal to anyway?
     
    Last edited: Apr 28, 2015
  5. Apr 28, 2015 #4

    SammyS

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    Indeed !

    What is ƒ(-2) equal to?

    What is ƒ ?

    You were considering finding L(1) .

    That makes ƒ(x) = 1, a constant function, so it maps everything to 1. It even maps -2 to 1.
     
  6. Apr 28, 2015 #5
    I think i understand.

    L(1) means that we are considering the function f(x) = 1 (a straight line through y=1):

    L(f) = f' + f(-2)t

    L(1) = d(1)/dt + f(-2)t

    f(-2) is equal to 1 in this case, so:

    d(1)/dt + f(-2)t = 0 +t = t





    However, if we consider L(t):

    L(t) = t' + f(-2)t
    =d(t)/dt + f(-2)t
    = 1 + f(-2)t

    in this case, we are considering f(x) = t, another constant function (y=t throughout), so f(-2) = t:

    L(t) = 1 + f(-2)t = 1 + t*t

    = 1 + t^2

    this does not equal 1+(-2)t as indicated in the markscheme.


    EDIT: nvm, i understand now.

    if f(t) = t then:

    f(-2) = -2.

    Plug it all in and it all works.

    thanks,
     
    Last edited: Apr 28, 2015
  7. Apr 28, 2015 #6

    can you look at my edit? thanks.
     
  8. Apr 28, 2015 #7

    SammyS

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    Yup.

    (I quickly deleted a post I had made in reply. Now that you edited that post, all is well.)
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Simple matrix/linear algebra question, help
Loading...