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Matrix cofactor problem

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

    Let A =

    [ 3 2 ]
    [ 6 7 ]

    Find the following:

    (a) det (A) = __

    (b) the matrix of cofactors C = (__, __) (__, __)

    (c) adj (A) = (__, __) (__, __)

    (d) A^-1 = (__,__) (__, __)

    2. Relevant equations
    I am just not to familiar with what cofactor means, and adj(A), A^-1, as well as det(A).
    How can I find all that from one matrix?

    3. The attempt at a solution

    I put the matrix into RREF, but for the determinant don't I have to like multiply diagonally or something?

    Thank YOU!
     
  2. jcsd
  3. Mar 10, 2009 #2

    Delphi51

    User Avatar
    Homework Helper

  4. Mar 10, 2009 #3
    these are really simple for a 2 by 2 matrix. You're given the matrix A, and they ask for you det(A), matrix cofactors, adj(A), and A^-1.

    det(A) means the determinant of A.

    adj(A) means the adjugate matrix of A.

    A^-1 means the inverse of A.

    I'll get you started on the determinant. The determinant of a 2 by 2 matrix [a b]/ [c d]


    is ad-bc
     
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