1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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


    User Avatar
    Science Advisor
    Homework Helper

    Pick A be the identity matrix. Interchange two rows. Have you tried any numerical examples at all?
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook