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Linear algebra span of?

  1. Jan 16, 2012 #1
    1. The problem statement, all variables and given/known data
    I do understand that in matrix 3x2, the set of vector doesn't span of R3. What should I do to make the set of vector span of R3.


    2. Relevant equations



    3. The attempt at a solution
    I think adding one more set of vector is the best idea. So, if I can add one more set of vector to make them span of R3, how to find the third set of vector. thanks
     
  2. jcsd
  3. Jan 16, 2012 #2
    I think you need to state the question more clearly. In a 3x2 matrix the columns don't span R^3. The three standard vectors (1,0,0), (0,1,0), (0,0,1) span R^3. I you want to make a matrix of which the colums span R^3 put these in a matrix.

    If you want to use the two vectors you already got from the matrix:
    - first check to see if the two you have are linearly independent.
    i.e. whether one is a mulitple of the other (in the case of 2 vectors)
    - If they are find a third vector that is also linearly independt of both the vectors (together)
    - I they aren't find two more that, together with one of the vectors you already had,
    are linearly independent of each other.

    Then put them in a matrix.
     
  4. Jan 16, 2012 #3
    I mean if we got 2 vector a = (1,2,1) and b = (1,3,1). Then I need to create one more vector that will make the set of vectors span of R3
     
  5. Jan 17, 2012 #4
    There are many way's to do this. One way is to put these to vectors and (a,b,c) in a matrix. Calculate the determinant then choose a,b,c such that the determinant is not 0. Any such a,b,c will do
     
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