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Math Help - methods in working out the identity of a matrix

  1. #1
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    Question methods in working out the identity of a matrix

    how would i work out the identity of the matrixs
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  2. #2
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    Quote Originally Posted by npm1 View Post
    how would i work out the identity of the matrixs
    In the first instance, you go to your class notes and textbook and review the theory and relevant examples. Use Google if necessary to fnd these things. MHF is not a teaching website designed to provide instruction with such broad questions.

    In the second instance you post the specific matrix you are having trouble with. Show what you have tried and say where you are stuck.
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  3. #3
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    Quote Originally Posted by npm1 View Post
    how would i work out the identity of the matrixs
    You don't. There is no such thing as the "identity of a matrix". The n by n "identity matrix" is the matrix having "1"s on the diagonal and "0" everywhere else. You don't need to "work" that out!

    Do you mean the inverse of a matrix? There are a number of different methods for doing that, all very long and complicated. For example, if we let " B_{ij}" be the "minor" of matrix A, that is, the determinant we get if we remove the ith row and jth column from A, multiplied by (-1)^{i+j}, then the inverse of matrix A has i,j component B_{ji} divided by the determinant of matrix A.

    Simpler, in my opinion is to write matrix A and the identity matrix side by side, then "row-reduce" A to the identity matrix while applying the same row operations to the matrix beside A. When you have reduce A to the identity matrix, the identity matrix will have been reduced to the inverse of A.
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