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Math Help - LinAlg - Determinants/Adjoints?

  1. #1
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    LinAlg - Determinants/Adjoints?

    If A is 3x3 and detA=2, then det(A^-1-(adjA)) = ?

    I know that the answer is -(1/2)
    and my teacher did it on the board, saying that adjA=(detA)(A^-1)

    but I don't understand that part of it!
    i'd really appreciate it if someone would explain it to me

    thanks in advance
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  2. #2
    o_O
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    Use these facts:
    • \det(AB) = \det (A) \cdot \det (B)
    • \det(A^{-1}) = \frac{1}{\det (A)}
    • \det (cA) = c^n \det (A) where c is a constant, n is the size of the matrix
    • \det \left( \text{adj} (A)\right) = \left[\det (A)\right]^{n-1} ..... Can be shown here


    ______________

    You should know that: A^{-1} = \frac{1}{\det (A)} \cdot \text{adj} (A)

    Multiply both sides by \det (A) to get: \det (A) \cdot A^{-1} = \text{adj} (A)
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