Vectors and Matrices problem

Discussion in 'Math' started by Malsch, Dec 10, 2011.

  1. Malsch

    Thread Starter New Member

    Mar 19, 2011
    23
    0
    Hi,

    I have the following situation: w = px + qy + rz = qi - 5qj - 11pk
    where w, x, y and z are vectors and:
    x = 4i + 2j - 3k
    y = 5i - 3j + 8k
    z = -2i - j + 4k

    i need to find all the possible values of p, q and r.

    I substituted x, y and z in the first equation and compared coefficients of i, j and k and ended up with the following equations:

    4p + 4q - 2r = 0
    2p + 2q - r = 0
    8p + 8q +4r = 0

    This implies that one solution is obviously 0 for all the 3 unknowns. I really do not know how to continue from here. i used gaussian elimination and ended up with the following matrix:

    (4 4 -2 | 0)
    (0 0 0 | 0)
    (0 0 8 | 0)

    Any help would be greatly appreciated. 10q :)
     
  2. Tesla23

    Active Member

    May 10, 2009
    318
    67
    (0 0 8 | 0) means that r=0
    (4 4 -2 | 0) then gives p=-q

    so the general solution is (p,q,r) = (a, -a, 0) for any value 'a'
     
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