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Math Help - Matrix question

  1. #1
    Junior Member
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    Matrix question

    I am not sure exactly, what they are asking me to do, i found a set of numbers that works for this system but its not accepting my answer, which makes me think they are asking for variables? not realy sure


    Solve this system:



    X1 = | | + | |S
    X2 = | | + | |S
    X3 = | | + | |S
    X4 = | | + | |S
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  2. #2
    MHF Contributor
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    Hi

    The determinant of the matrix is 0
    You can find all variables as functions of only one parameter
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  3. #3
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    Sorry but i dont understand what you mean by that statement, can you clarify?
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  4. #4
    MHF Contributor

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    The fact that the determinant, \left|\begin{array}{cccc}1 & 1 & 0 & 0 \\ 0 & 1 & 1 & 0 \\ 0 & 0 & 1 & 1 \\ 1 & 0 & 0 & 1\end{array}\right| is 0 means the equations are not independent- either there is no solution or there are an infinite number of solutions. If there are an infinite number of solutions, you cannot solve for all 4 variables but rather can solve for three of them in terms of the fourth. For example, from the first equation, x_2= 3- x_1 and, from the fourth, x_4= 12- x_1. Now, put those into the second or third equation to find x_3 the same way. Try both equations to make sure you get the same result so that there is a solution.

    Those are the numbers that go into the squares. Letting the parameter, S, be x_1, the first row is x_1= 0+ 1 S and the second row would be x_2= 3- 1 S. Now, be aware that you could solve for any three of the variables in terms of the fourth and use that as the parameter, S, so there is NOT one single answer. You appear to be using a computer system to input your answer and I have no idea how it will handle the different possible answers. That's one reason I dislike those things.
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  5. #5
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    ah i understand now, thanks alot
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