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Some linear algebra problems i need help with

  1. Mar 24, 2009 #1
    Let A and B be nxn matrices.
    1. Suppose that AB=AC and det A does not equal 0. Show that B=C

    2. Show that A is nonsingular if and only if A transpose is nonsingular.

    3. Show that det AB = det BA.

    4. Show that det AB = 0 if and only if det A=0 or det B=0

    5. Show that if AB= -BA and n is odd, then A or B is singular.

    6. Show that det A*Atranspose is greater than equal to 0

    7. Show that det A*Btranspose = det Atranspose* det B

    8. Let A be nxn skew-symmetric matrix. If n is odd, show that det A=0

    9. Show that 3x3 vandermonde matrix has a determinant equal to (a-b)(b-c)(c-a) The matrix is
    [1 1 1
    a b c
    a^2 b^2 c^2]
    Thank you.


    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Mar 24, 2009 #2
    No one is going to give you the answer without any work. Do your own homework and ask for help here if you need it
     
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