Co factor

  • Thread starter ajayguhan
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  • #1
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Main Question or Discussion Point

In a matrix the sum of element of a matrix in a row times it's co factor of that elemt gives the determinant value, but why does the sum of element of a matrix times cofactor of different row is always zero?
 

Answers and Replies

  • #2
Erland
Science Advisor
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In a square matrix A, replace row j by row i, obtaining a new matrix B with row i and row j being equal. Expanding using elements from row i in A and cofactors corresponding to row j in A will be the same as expanding det B along row j (using cofactors corresponding to row j in B also) since the elements and cofactors are the same in both cases. So the result is det B, which is...?
 
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