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Math Help - First Year Linear Algebra Assignment Question

  1. #1
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    First Year Linear Algebra Assignment Question

    I dont know how to go about doing this, well i know how to find the conditions but the answer i come up with is in a different format than the input for the online assignment is heres the question

    Find conditions that the b's must satisfy for the system to be consistent


    (the actual system is in the attached file underneath)




    and then the format for the answer is
    b1=_____b2+______b3

    (the 1, 2, and 3 are in subscript)
    Attached Thumbnails Attached Thumbnails First Year Linear Algebra Assignment Question-session.quest131139entrance1_n10044.gif  
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  2. #2
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    Try to solve the equations for x_1, x_2, and x_3. (row reducing the augmented matrix works nicely.) That will reduce to an equation involving the "b"s. Solve that equation for b_1.
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  3. #3
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    I reduced it to row-echlon form
    so like
    1 0 0
    0 1 0
    0 0 1
    and that gave me values for x1, x2, and x3
    but they dont go into each other at all so theres no way to solve for b1

    i saw a solution in my book similar to this but what happens in the book is that one of the rows in the matrix becomes all 0's and so you set the b's in that specific row to 0 and then solve for b1 and that gives you an answer, BUT the problem is i tried getting one of the rows to zero and it wont work out
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  4. #4
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    Changing the variables to ease typing(!):

    a - 5b + 4c = u [1]
    25a - 29b + 28c = v [2]
    -6a + 6b - 6c = w ; -a + b - c = w/6 [3]

    Add [1] and [3] to get -4b + 3c = u + w/6 [4]
    Multiply [3] by 25, then add to [2] : -4b + 3c = v + 25w/6 [5]

    [4]and[5]: u + w/6 = v + 25w/6
    simplify: u = v + 4w .... in your case: b1 = (1)b2 + (4)b3

    S'that what you're after?
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