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Matrix question

  1. Apr 30, 2009 #1
    Matrix A:

    1 2 4 1
    2 4 8 2
    3 1 5 7

    The question says find a basis for the solution set AX=0, X is the vector of variables
    [x1,x2,x3,x4]^t

    What is a basis? and how can i approach this problem?
     
  2. jcsd
  3. May 1, 2009 #2

    Mark44

    Staff: Mentor

    By inspection, I can see that the solution space for the equation AX = 0 will be at least a one-dimensional subspace of R4 (i.e., a line through the origin), and on closer inspection I can see that this solution space will be a two-dimensional subspace of R4, a plane through the origin.

    You asked what a basis is. Isn't that term defined in your textbook? What this problem is asking for is a set of vectors that spans the solution space. IOW, a set of vectors such that any solution vector is a linear combination of the basis vectors.

    You should also look up the definitions of the terms I have underlined.
     
  4. May 1, 2009 #3

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    Solve the equations x+ 2y+ 4z+ u= 0, 2x+ 4y+ 8z+ u= 0, and 3x+ y+ 5z+ 7u= 0. There is, of course, an infinite number of solutions so instead of a single solution you will get equations expressing some of the variables in terms of the others. Choose simple values for those "others" and solve for the rest.
     
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