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There are many useful applications of the determinant. Cofactor expansion is one technique in computing determinants.
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Hello There are many useful applications of the determinant. Cofactor expansion is one technique in computing determinants. Now, we discuss how to find these cofactors through minors of a matrix and use both of these elements to find the adjoint of A. Then by the adjoint and determinant, we can develop a formula for finding the inverse of a matrix. Minors: To find the minors of any matrix, expand block out every row and column one at a time until all the minors are found. Steps to Finding Each Minor Of A Matrix: 1. Delete the i th row and j th column of the matrix. 2. Compute the determinant of the remaining matrix after deleting the row and column of step 1. Example: Find the minors of the matrix              1 1 1 2 1 1 1 1 2 . *Note: This step procedure just outlines finding the minor M 11 of the matrix. 1. Delete the i th row and j th column of the matrix.              1 1 1 2 1 1 1 1 2 2. Compute the determinant of the remaining matrix after deleting the row and column of step 1. ( 1)( 1) (1)(1) 0  1 1 1 1 det 1 1 1 2 1 1 1 1 2 11                            M Using the same steps above, the other minors of the matrix are given below. 3 1 1 2 1 det 12         M  3 1 1 2 1 det 13         M  1 1 1 1 2 det 21          M  3 1 1 1 2 det 22         M  2 1 1 1 1 det 23        M  1 1 1 1 2 det 31         M   3 2 1 1 2 det 32        M  1 2 1 1 1 det 33         M  Thus, the minor matrix is given by                1 3 1 1 3 2 0 3 3 M Cofactors: To find the cofactors of a matrix, just use the minors and apply the following formula: C ij = (-1) i + j M ij where M ij is the minor in the i th row, j th position of the matrix. Example: Find the cofactors of the matrix     

Jul 23, 2017

#### sdcs-01

Jul 23, 2017
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