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Thread: Determinant and inverse matrix

  1. #1
    kym
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    Determinant and inverse matrix

    Last edited by kym; Oct 28th 2017 at 08:56 AM.
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    kym
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    Re: Determinant and inverse matrix

    How do i solve this question? I have been trying it for a hour and the answers i got didnt match any of the options... I already used A^-1=1/|A|*A^^ but the element c(1,4) is 0 to me dont know why...
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    Re: Determinant and inverse matrix

    Quote Originally Posted by kym View Post
    How do i solve this question? I have been trying it for a hour and the answers i got didnt match any of the options... I already used A^-1=1/|A|*A^^ but the element c(1,4) is 0 to me dont know why...
    $A^{-1}_{1,4} = \dfrac{(-1)\left | \begin{pmatrix}2 &0 &-1 \\0 &1 &-4 \\1 &0 &0 \end{pmatrix}\right|}{|A|} = -\dfrac{1}{4}$

    $\begin{pmatrix}2 &0 &-1 \\0 &1 &-4 \\1 &0 &0 \end{pmatrix}$ is the minor matrix of $A_{4,1}$

    $(-1) = (-1)^{1+4}$ turns the minor into a cofactor
    Last edited by romsek; Oct 28th 2017 at 10:10 AM.
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    kym
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    Re: Determinant and inverse matrix

    Quote Originally Posted by romsek View Post
    $A^{-1}_{1,4} = \dfrac{(-1)\left | \begin{pmatrix}2 &0 &-1 \\0 &1 &-4 \\1 &0 &0 \end{pmatrix}\right|}{|A|} = -\dfrac{1}{4}$

    $\begin{pmatrix}2 &0 &-1 \\0 &1 &-4 \\1 &0 &0 \end{pmatrix}$ is the minor matrix of $A_{4,1}$

    $(-1) = (-1)^{1+4}$ turns the minor into a cofactor
    What formula is that? I thought that above the determinant of A i had to use the adjugate matrix of A and find the element {1,4}. How can you use just A4,1 to solve that if it isn't even a matrix to stand above the determinant? I'm so confused with determinants in general :/...
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    Re: Determinant and inverse matrix

    Quote Originally Posted by kym View Post
    What formula is that? I thought that above the determinant of A i had to use the adjugate matrix of A and find the element {1,4}. How can you use just A4,1 to solve that if it isn't even a matrix to stand above the determinant? I'm so confused with determinants in general :/...
    think about the steps you need to find the inverse matrix

    first you find the determinant of each element's minor matrix

    then you apply the sign correction to convert the minor determinants to cofactors

    then you divide by the determinant of the original matrix

    then you transpose the elements

    so for element (1,4) of the inverse we need to calculate element (4,1) of the cofactor matrix and divide by the determinant of the original matrix.

    that's exactly what this does.

    I didn't get any formula anywhere. I just understand how the inverse is computed using the cofactor method.
    Thanks from topsquark and kym
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  6. #6
    kym
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    Re: Determinant and inverse matrix

    Quote Originally Posted by romsek View Post
    think about the steps you need to find the inverse matrix

    first you find the determinant of each element's minor matrix

    then you apply the sign correction to convert the minor determinants to cofactors

    then you divide by the determinant of the original matrix

    then you transpose the elements

    so for element (1,4) of the inverse we need to calculate element (4,1) of the cofactor matrix and divide by the determinant of the original matrix.

    that's exactly what this does.

    I didn't get any formula anywhere. I just understand how the inverse is computed using the cofactor method.
    Thanks a lot man! I don't knew we could use such methods to do so... I was guiding myself only by the formulas.

    I'm having algebra exam in less than a week, if you dont mind, could you give some youtube channel or nice study material to prepare myself better? Would apreciate the help.
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