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Easy matrix/determinants question

  1. Feb 11, 2009 #1
    1. The problem statement, all variables and given/known data

    Suppose A and B are 3 x 3 matrices and det A = x ≠ 0 while det B = y. Let
    C be the matrix ((2A)^-1 )B <-- (2A) inverse x B

    then det C is:

    2. Relevant equations


    3. The attempt at a solution

    det(2A) = 2x, so det 2A inverse = 1/(2x)
    det C = y/(2x)...which is not one of the solutions

    a) y/8x b) 2xy c) -2y/x d) 2y/x e) 8y/x

    what am I missing here?
     
  2. jcsd
  3. Feb 11, 2009 #2
    You are very close; however,

    [tex]\det(\alpha A)=\alpha^{n} \det(A)[/tex]

    where n is the order of the matrix A, in this case 3. To understand why this happens, think of the determinant of the identity and multiply it by a scalar.
     
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