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Matrices problem

  1. Apr 20, 2009 #1
    x1[0,0,0] + x2[1,1,0] + x3[0,1,0] + x4[-1,-1,0] + x5[0,0,1] + x6[1,0,-1] = [4,0,2]

    ** left to right is top to bottom **


    I am first asked to find 3 columns that span R3, I found that [-1,-1,0],[0,0,1],[1,0,-1] span r3 because they have a non-zero determinant. Now the next question is where i have trouble

    I am asked to express the right side as a linear combination of the three columns i chose?

    How can i write the three columns as a linear combination? I havent been able to find any really good explanation of a linear combination, can ne one help?
     
  2. jcsd
  3. Apr 20, 2009 #2

    CompuChip

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    It just means, find three numbers a, b, c such that
    a [-1, -1, 0] + b [0, 0, 1] + c [1, 0, -1] = [4, 0, 2]

    The left hand side is called a linear combination of [-1, -1, 0], [0, 0, 1] and [1, 0, -1].
     
  4. Apr 20, 2009 #3
    ok then if i've done this correctly it should be:

    0*[-1,-1,0] + 6*[0,0,1] + 4*[1,0,-1] = [4,0,2]

    a=0
    b=6
    c=4
     
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