Linear algebra question

  • #1
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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?
 
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Answers and Replies

  • #2
761
13
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.
 
  • #3
HallsofIvy
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Homework Helper
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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].
 
  • #4
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[itex]
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)
[/itex]
[itex]
x=b1,b2,b3

[/itex]

[itex]
g(b1,b2,b3)= a_1g_1(b1,b2,b3)+ a_2g_2(b1,b2,b3)+ a_3g_3(b1,b2,b3)
[/itex]

what is the next step
for constracting the equations
 
  • #5
HallsofIvy
Science Advisor
Homework Helper
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There is NO "[itex]g(b2, b3,b3)[/itex]! Set x equal to b1, b2, and b3 separately to get three equations.
 
  • #6
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0
like this?

X(1,2,0)+y(0,1,2)+z(0,0,1)=(1,2,5)
 

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