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Unformatted text preview: cofactor of A at aij is the number Cij = (−1)i +j |Aij |.
The matrix C = [Cij ] is called the matrix of cofactors of A.
The matrix adj(A) = C T is called the classical adjoint of A. Outline The Classical Adjoint A Formula for the Inverse of a Matrix Example Example
Find the classical adjoint of the matrix 100
A= 2 3 0 456 Cramer’s Rule Eigenvalues Outline The Classical Adjoint A Formula for the Inverse of a Matrix Cramer’s Rule Eigenvalues A Preliminary Result
Suppose A = [aij ] is an n × n matrix with cofactor Cij at aij . Then
for any 1 ≤ i , j ≤ n,
n det A if i = j
if i = j aik Cjk =
k =1 Proof.
If i = j , then the sum is det A.
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