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anonymous

  • 5 years ago

Quick question...I'm given the matrix of the inverse, how do I directly calculate det(A) from this?

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  1. anonymous
    • 5 years ago
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    det(inverse of A) = 1/det(A)

  2. anonymous
    • 5 years ago
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    seriously? cool, I'll try it out thanks!

  3. anonymous
    • 5 years ago
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    yes, you're welcome

  4. anonymous
    • 5 years ago
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    its a 4x4 matrix if thatchanges things

  5. anonymous
    • 5 years ago
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    it can be used on 4x4, 3x3, etc

  6. anonymous
    • 5 years ago
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    k cool

  7. anonymous
    • 5 years ago
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    but i dont think finding the determinant of 4x4 matrix easy. in my school the problem is usually 2x2 or 3x3

  8. anonymous
    • 5 years ago
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    Where does this equation come from? Is it unique, or does it derive from something else? It seems that it follows from A^-1=1/A..and the answer was right using the equation

  9. anonymous
    • 5 years ago
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    i forgot where it came from. it was on my notebook. my teacher gave it to me some months ago, along with : det(transpose of A) = det (A)

  10. anonymous
    • 5 years ago
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    yeah that one I knew, I'll have to look over my notes I think

  11. anonymous
    • 5 years ago
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    MathTy, I worked it out last night. The determinant of this 4x4 is 1! :D

  12. anonymous
    • 5 years ago
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    @MathTy: \[A*A^{-1}=I \implies \det(A*A^{-1})=\det(I) \implies \det(A)*\det(A^{-1})=1\]\[\implies \det(A^{-1})=1/\det(A).\] :)

  13. anonymous
    • 5 years ago
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    awesome I found it to be 1, but not nicely put like this. Does that mean that all invetible matrices have det=1?

  14. anonymous
    • 5 years ago
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    What do you mean "not nicely put like this"? xD That little proof just means that the product of the determinants of the regular matrix and the inverse matrix is always equal to 1. Not necessarily that the determinant of all invertible matrices is 1 -- this is just a clean exception. :P

  15. anonymous
    • 5 years ago
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    oh ok, by simple like this I just mean that to find the determinant I used cofactors to break it down into a3x3 matrix, then used rule of Sarrus to get the det of the 3x3, which came to 1

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