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Math Help - General Solution/ Vectors

  1. #1
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    General Solution/ Vectors

    I have this matrix:
    1 2 -2 -1 0
    2 3 -5 1 -7 0
    0 1 1 -1 1 0
    -1 1 5 -1 0 0

    I solve for row echelon form:

    1 2 -2 -1 0 0
    0 1 1 -1 0 0
    0 0 0 1 -3 0
    0 0 0 0 0 0

    I'm supposed to find the general solution of this as well a set of vectors that span the solution space.

    Therefore,
    x5= t1

    x4= -3x5
    x4= -3(t1)

    x3= (t2)

    x2 + x3 - x4=0
    x2= 3(t1) - (t2)

    x1+ 2x2 - 2x3 - x4 = 0
    x1= 2(t2) - 3(t1) - 2(3(t1)-(t2))
    x1= 4(t2) - 9(t1)


    So I get:
    x1= 4(t2) - 9(t1)
    x2= 3(t1) - (t2)
    x3= (t2)
    x4= -3(t1)
    x5= (t1)

    (x1, x2, x3, x4, x5)= t1(-9, 3, 0, -3, 1) + t2 (4, -1, 1, 0, 0)

    And the general solution would be:
    x1 =[-9] [4]
    x2 = [3] [-1]
    x3 =t1[0]+t2[1]
    x4 = [-3] [0]
    x5 = [1] [0]
    Sorry about the messy writing, I'm not sure how to write matrices on a computer. I think that is correct, can anyone verify?
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  2. #2
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    Quote Originally Posted by Hellreaver View Post
    I solve for row echelon form:

    1 2 -2 -1 0 0
    0 1 1 -1 0 0
    0 0 0 1 -3 0
    0 0 0 0 0 0
    Get it to row-reduced echelon form first.
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