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Linear algebra: determinants (proof)

  1. Apr 10, 2006 #1
    hi, i seem to have some trouble proving:

    Suppose M = [A B:O C], where A is a kxk matrix, C is a pxp matrix, and O is a zero matrix. Show that det(M) = det(A)det(C).

    my attempt at a proof:

    det(M) = det(A)det(C)

    det[A B:O C] = det(A)det(C)

    AC - OB = det(A)det(C)

    AC = det(A)det(C) <-- doesn't make sense!

    please point out where my logic failed.
  2. jcsd
  3. Apr 10, 2006 #2
    nevermind. i figured out where i went wrong (i treated the matrices as if they were scalar, stupid me). thanks for all the help :sarcasm:
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