This is sometimes referred to as the adjoint matrix. The final result of this step is called the adjugate matrix of the original.They are indicators of keeping (+) or reversing (-) whatever sign the number originally had. The (i, j) - minor of A, denoted Mij, is the determinant of the (n 1) × (n 1) matrix that results from deleting row i and column j of A. Note that the (+) or (-) signs in the checkerboard diagram do not suggest that the final term should be positive or negative. Compute the inverse of this matrix by computing its classical adjoint and determinant. Definition edit The adjugate of A is the transpose of the cofactor matrix C of A, In more detail, suppose R is a unital commutative ring and A is an n × n matrix with entries from R. Continue on with the rest of the matrix in this fashion. The third element keeps its original sign. When assigning signs, the first element of the first row keeps its original sign.You must then reverse the sign of alternating terms of this new matrix, following the “checkerboard” pattern shown. Thus, the determinant that you calculated from item (1,1) of the original matrix goes in position (1,1). Place the results of the previous step into a new matrix of cofactors by aligning each minor matrix determinant with the corresponding position in the original matrix.
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