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Matrix Determinant Question

  1. Oct 10, 2009 #1
    1. The problem statement, all variables and given/known data

    Let A, B and C be 3 x 3 invertible matrices where det A = -2 ,det B = -2 and det C is some non-zero scalar.

    Then det (CTA−1B2C−1) = ?

    and det [ −2(A2)TC2B−1(C−1)2] = ?

    the T represents transpose and the -1 represents inverse.

    2. Relevant equations

    What does the non-zero scalar mean?

    3. The attempt at a solution

    I used the rule to expand the products of the determinants, but I'm not sure what to do next and what it means by non-zero scalar.
     
  2. jcsd
  3. Oct 10, 2009 #2
    When you find the determinant of a matrix, your result is a scalar, or a single number. Non zero just means that det(c) is a scalar other than zero.
     
  4. Oct 10, 2009 #3
    So how would it affect my answer since I really don't know the value of det(c).
     
  5. Oct 10, 2009 #4

    Mark44

    Staff: Mentor

    Do you know any theorems about determinants? One that I remember is that det(AT) = det(A). You'll need some of these theorems in these problems, particularly one for det(A-1) as it relates to det(A), and one for det(An) as it relates to det(A).

    Tip: To make exponents (for transposes and matrix inverses), click the Go Advanced button below the text entry field. This opens a menu of buttons you can use to format what you write. The X2 button can be used for exponents and the X2 button can be used for subscripts.

    Here are your problems, formatted for easier reading:
    a) det(CTA−1B2C−1)
    b) det( −2(A2)TC2B−1(C−1)2)
     
  6. Oct 11, 2009 #5

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    For these problems the most crucial thing you need to know is that det(AB)= det(A)det(B). If you know that, these problems are easy. If you don't, ---.
     
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