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Math Help - Trying to apply matrices in Physics but having trouble

  1. #1
    s3a
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    Trying to apply matrices in Physics but having trouble

    Here is the original matrix:
    matrix([20,10,0,0,549/100],[0,-10,30,30,41/50],[20,0,30,30,467/100],[1,-1,-1,0,0])

    Here is the matrix in its echelon form:
    matrix([1,1/2,0,0,549/2000],[0,1,2/3,0,183/1000],[0,0,1,9/11,303/11000],[0,0,0,0,1])

    (The last column is for the constants on the right of the augmented line of the matrix).

    Sorry for the dumb question but can someone please help me extrapolate the values of x1, x2, x3, and x4 given this information?

    Any help would be greatly appreciated!
    Thanks in advance!
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  2. #2
    Member rtblue's Avatar
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    If I have interpreted the question correctly, the solution is as follows:

    \displaystyle x_1+\frac{1}{2}x_2+0(x_3)+0(x_4) = \frac{549}{2000}

    \displaystyle 0(x_1) + x_2+\frac{2}{3}x_3+0(x_4)= \frac{183}{1000}

    \displaystyle 0(x_1)+0(x_2)+x_3+\frac{9}{11}(x_4) = \frac{303}{11000}

    Now, I run into a problem, but first let me explain to you what I've done. Each of the four columns (not including the constant column) corresponds to x1,x2,x3, and x4. The first column is x1, the second column is x2, the third column is x3, and the fourth column is x4. Look at the first row (That is the first equation). The first number in the first row is 1, and since this is in column one, we multiply this by x1. Now we add to that: the second number in the first row is 1/2 ,and since this is in the second column we multiply that by x2. We continue similarly all through the matrix.

    The problem I encountered was in the last row. The fourth element should not be zero. In this case, only the first three elements of the last row should be zero.With the numbers you've given, we have 0+0+0+0=1 and this is obviously wrong. Have you made a typo?
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  3. #3
    s3a
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    Firstly, sorry if I sound rude for some reason, it's just I'm dead tired and burnt out so I'm a wreck.

    On to the issue, I think I instead just made the matrix wrong. Your answer is wrong but it's very likely my fault.

    I1 = x1
    I2 = x2
    I3 = x3
    I4 = x4

    Here are my equations. My friend said the fact that I3 = I4 (x3 = x4) means I HAVE TO treat it as one variable but I think that the matrix will "sort this out itself" if I just put them as two different variables even if they're the same. Again, I'm burnt out because of a lot of other work and I have this due tomorrow so I'm not in the best state to "argue" but I'm feeling like I'm right.

    Here are the equations:
    5.49 = 20I1 + 10I2
    30I3 + 30I4 - 10I2=-0.82
    30I3 + 30I4 + 20I1=4.67
    I1 - I2 - I3 = 0

    Please help!
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  4. #4
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    Quote Originally Posted by s3a View Post
    Firstly, sorry if I sound rude for some reason, it's just I'm dead tired and burnt out so I'm a wreck.

    On to the issue, I think I instead just made the matrix wrong. Your answer is wrong but it's very likely my fault.

    I1 = x1
    I2 = x2
    I3 = x3
    I4 = x4

    Here are my equations. My friend said the fact that I3 = I4 (x3 = x4) means I HAVE TO treat it as one variable but I think that the matrix will "sort this out itself" if I just put them as two different variables even if they're the same. Again, I'm burnt out because of a lot of other work and I have this due tomorrow so I'm not in the best state to "argue" but I'm feeling like I'm right.

    Here are the equations:
    5.49 = 20I1 + 10I2
    30I3 + 30I4 - 10I2=-0.82
    30I3 + 30I4 + 20I1=4.67
    I1 - I2 - I3 = 0

    Please help!
    Taking your equations and running rref yields:

    x_1=x_2=.183, \ x_3=-1\times 10^{-15}, \ x_4=.033666666666...

    However, from both your posts, I have no idea what is going on so maybe this will help.
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  5. #5
    A Plied Mathematician
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    ...I have this due tomorrow...
    Sounds like this problem is counting towards a final grade. Thread closed.
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  6. #6
    Flow Master
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    Quote Originally Posted by Ackbeet View Post
    Sounds like this problem is counting towards a final grade. Thread closed.
    Yes. Rule #6 here: http://www.mathhelpforum.com/math-he...hp?do=vsarules
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