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Math Help - Calculate the solution using X = A^-1B

  1. #1
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    Calculate the solution using X = A^-1B



    I wrote the system of equations in the form AX = B, however how would I go about calculating the solution using the equation X = A^-1B?
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  2. #2
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    Re: Calculate the solution using X = A^-1B

    Go to this web page.
    Scroll about half way down.
    You will find material of inverses of a 2\times 2 matrix.
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  3. #3
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    Re: Calculate the solution using X = A^-1B

    You would find the inverse of the matrix and multiply by it! That is exactly what A^{-1}B means.

    The inverse of the two by two matrix [tex]\begin{bmatrix}a & b \\ c & d\end{bmatrix} is \frac{1}{\Delta}\begin{bmatrix}d & -b \\ -c & a\end{bmatrix} where \Delta= ad- bc, the determinant of the matrix. Be sure to do the multiplication in the order shown.
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  4. #4
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    Re: Calculate the solution using X = A^-1B

    if AX = B

    then A^{-1}(AX) = A^{-1}B so

    (A^{-1}A)X = A^{-1}B, that is:

    IX = X = A^{-1}B.

    so if A is indeed invertible, then calculating A^{-1}B tells you which vector "X" is.
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