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Determinant functions

  1. Nov 22, 2008 #1
    1. The problem statement, all variables and given/known data

    Let A be a 3 x 3 matrix. Consider the function f(A) = a11a22a33; g(A) = a11 a12 a13 and h(A) =1. Show that each of these is not a determinant function.

    2. Relevant equations

    det(I) = 1
    det(B) = det(A) (if B is obtained from adding a mutiple of one row of A to another row)
    det(B) = - det(A) (if B is obtained from interchange two rows)
    det(B) = m det(A) (if B obtained from A by multiplying a row of A by the number m)

    3. The attempt at a solution
    isn't f(A) = a11a22a33 a determinant function ?
     
  2. jcsd
  3. Nov 22, 2008 #2
    Can you show that all four conditions are satisfied for f(.)?
     
  4. Nov 22, 2008 #3
    what to take as a reference, though?
     
  5. Nov 22, 2008 #4
    I don't understand what you mean by reference. You should be able to show that for any arbitrary matrix A= aij, if you do the things stated in the four conditions, f(.) behaves as a determinant function.

    To prove that f(.) is not a determinant function, a counterexample will suffice. Trying to prove that f() is a determinant function might help you come up with this counter-example.
     
  6. Nov 23, 2008 #5
    I understand determinants with numbers. but its confusing with variables. Can you give me a simple example please?
     
  7. Nov 23, 2008 #6
    An example please...
     
  8. Nov 23, 2008 #7

    Dick

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    Science Advisor
    Homework Helper

    Pick A be the identity matrix. Interchange two rows. Have you tried any numerical examples at all?
     
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