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Homework Help: What is the way of solving this question

  1. Dec 16, 2008 #1
    what is the general way of solving this question:

    http://img116.imageshack.us/img116/1152/25587465vv2.gif [Broken]

    Last edited by a moderator: May 3, 2017
  2. jcsd
  3. Dec 16, 2008 #2


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    Homework Helper

    1. You want V(k) to be linearly independent so that it will form a basis for R3. So that means if you interpret them as row vectors in a matrix and perform row reduction, the end result should be a matrix whose rank is 3. So what does the matrix being of full rank imply? And what values of k are suitable such that the matrix is of full rank?

    2. Firstly determine the solution space of U(k). Then [tex]span(U(k1)) \subseteq span(V(k2)) [/tex] if [tex]\forall v \ \text{where v is a vector in basis of U(k1)} \ , v \in span(V(k2))[/tex]. ie. try to express every vector in the basis of U(k1) as a linear combination of V(k2). Take note of when this is possible (ie. which values of k1 and k2 permit that).
  4. Dec 16, 2008 #3
    i think i solved part 1.
    but i dont know how to use part 1
    in order to solve 2

    http://img384.imageshack.us/img384/2546/55339538nk4.gif [Broken]
    Last edited by a moderator: May 3, 2017
  5. Dec 17, 2008 #4
    what is a solution space?

    i can find k values for which i get one solution
    infinite solution
    or no solution

    what is the definition of solution space in a parameter matrix?
  6. Dec 17, 2008 #5
    how do i find the solution vectors of U(k)?
  7. Dec 17, 2008 #6
    when you say
    "Firstly determine the solution space of U(k). "

    there are 3 types of solution?(depends on the values of K)
    no solution
    1 solution
    infinite solution
  8. Dec 17, 2008 #7
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