What is the difference between minors and cofactors in determinants?
Answer (1)
Minors and cofactors are closely related concepts in the calculation of determinants. The minor of an element in a matrix is the determinant of the submatrix that remains after removing the row and column containing that element. It is denoted as M ij for an element a ij . The cofactor, on the other hand, is the signed version of the minor. The cofactor of an element a ij is given by C ij =(-1) i+j M ij , where the factor (-1) i+j introduces a sign change depending on the position of the element in the matrix. Minors are used to calculate the determinant, while cofactors are used to expand the determinant and in the adjoint of a matrix.
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