Submatrices proof

buckaroobill

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Joined
Dec 16, 2006
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This problem was confusing me, so any help would appreciated. I guess the thing that is confusing me most is how to notate each submatrix.

Use row reduction to show that the determinant of the n by n matrix symbolically represented by
[A C
O B]

is |A||B|, where

A is an m by m submatrix,
B is an (n-m) by (n-m) submatrix
C is an m by (n-m) submatrix, and
O is an (n-m) by m zero submatrix.

The thing that is confusing me most about this proof is how to notate the submatrices A, B, C, and O.
 
So far, I've gotten that you can reduce both A and B to upper triangular matrices, but I'm a little confused about the rest...
 
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