1. Limited time only! Sign up for a free 30min personal 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!

Linear algebra question

  1. Dec 28, 2008 #1
    the question is in the link:
    http://img517.imageshack.us/img517/3830/70738563la6.gif [Broken]

    i know thats how i find coordinated(x,y,z) U=x*v1 +y*v2 +z+v3

    but i dont know how to build this structure here?
    Last edited by a moderator: May 3, 2017
  2. jcsd
  3. Dec 28, 2008 #2
    In imageshack you see a link below which is named "hotlink for forums", copy THAT link here and the picture will be directly shown in your post.
  4. Dec 28, 2008 #3


    User Avatar
    Science Advisor

    You have a groupm, B, containing three members, [itex]{b_1, b_2, b_3}[/itex] and the vector space of all functions from B to R. (you say only "group of functions" but it must be a vector space for this to make sense.) You are also given a "basis" for that vector space defined by [itex]g_i(b_j)[/itex] equals 1 if i= j, 0 otherwise. You are asked to write g, defined by [itex]g(b_1)= 1[/itex], [itex]g(b_2)= 4[/itex], [itex]g(b_3)= 5.

    Okay, you must have [itex]g(x)= a_1g_1(x)+ a_2g_2(x)+ a_3g_3(x)[/itex]. Set x= [itex]b_1, b_2, b_3[/itex] to get three very simple equations to solve for [itex]a_1, a_2, a_3[/itex].
  5. Dec 28, 2008 #4
    g(b_1)= 1
    g(b_2)= 4
    g(b_3)= 5
    g(x)= a_1g_1(x)+ a_2g_2(x)+ a_3g_3(x)


    g(b1,b2,b3)= a_1g_1(b1,b2,b3)+ a_2g_2(b1,b2,b3)+ a_3g_3(b1,b2,b3)

    what is the next step
    for constracting the equations
  6. Dec 28, 2008 #5


    User Avatar
    Science Advisor

    There is NO "[itex]g(b2, b3,b3)[/itex]! Set x equal to b1, b2, and b3 separately to get three equations.
  7. Dec 28, 2008 #6
    like this?

Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Threads - Linear algebra question Date
Subspace question May 9, 2016
Linear Algebra -- Projection matrix question Apr 25, 2016
Linear Algebra Question Sep 11, 2015
Linear Transformations, Linear Algebra Question May 10, 2015
Simple matrix/linear algebra question, help Apr 28, 2015