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Math Help - [SOLVED] Find inverse of A

  1. #1
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    [SOLVED] Find inverse of A

    Okay this doesn't make any sense. I have to find the inverse matrix by using a theorem in my textbook. This theorem uses the adjoint to find the inverse matrix.

    Unfortunately it's a 4x4 matrix so it will take me a while to do but there's something that isn't right.

    Here is the matrix A

    1 3 1 1
    2 5 2 2
    1 3 8 9
    1 3 2 2

    My textbook has the answer inverse of A as

    -4 3 0 -1
    2 -1 0 0
    -7 0 -1 8
    6 0 1 -7

    Okay, now I know how to do this. Let me know if I got this straight.

    Step 1: find the matrix of minors, all 16 of them.
    Step 2: find the cofactors according to sign charts
    Step 3: transpose the cofactor matrix to obtain adjoint of A
    Step 4: Find the determinant of the 4x4 matrix
    Step 5: 1/det A * adjoint A = inverse matrix of A

    If this is correct, can someone help me out finding minors of 4x4 matrices? I can do it for 3x3 but I have difficulty for 4x4, same goes for the determinants. I'm a little confused about the rules but I understand how it works in 3x3 matrices.

    Thank you.
    Last edited by thekrown; February 15th 2010 at 03:37 PM.
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  2. #2
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    Quote Originally Posted by thekrown View Post
    Okay this doesn't make any sense. I have to find the inverse matrix by using a theorem in my textbook. This theorem uses the adjoint to find the inverse matrix.

    Unfortunately it's a 4x4 matrix so it will take me a while to do but there's something that isn't right.

    Here is the matrix A

    1 3 1 1
    2 5 2 2
    1 3 8 9
    1 3 2 2

    My textbook has the answer inverse of A as

    -4 3 0 -1
    2 -1 0 0
    -7 0 -1 8
    6 0 1 -7

    Okay, now I know how to do this. Let me know if I got this straight.

    Step 1: find the matrix of minors, all 16 of them.
    Step 2: find the cofactors according to sign charts
    Step 3: transpose the cofactor matrix to obtain adjoint of A
    Step 4: Find the determinant of the 4x4 matrix
    Step 5: 1/det A * adjoint A = inverse matrix of A

    If this is correct, can someone help me out finding minors of 4x4 matrices? I can do it for 3x3 but I have difficulty for 4x4, same goes for the determinants. I'm a little confused about the rules but I understand how it works in 3x3 matrices.

    Thank you.

    For minors of ANY square matrix "erase" one row and one column, exactly as you do for 3x3 or whatever...what is the problem?

    Tonio
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  3. #3
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    Okay I was a little confused. I thought you had to take into account the element as well when working on 4x4 matrices.
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