20.This paper elaborates several features of the sum of the cofactor of a determinant and provides the method to calculate the determinant of a Matrix by the sum of the cofactor of a determinant. 给出有关代数余子式之和的几个性质并予以证明,且给出利用代数余子式之和计算行列式的方法。
Then determinant formula of matrix A is as follows.|A| = a11(−1)1+1∣∣∣a22a23a32a33∣∣∣+a12(−1)1+2∣∣∣a21a23a31a33∣∣∣+a13(−1)1+3∣∣∣a21a22a31a32∣∣∣a11(−1)1+1|a22a23a32a33|+a12(−1)1+2|a21a23a31a33|+a13(−1)1+3|a21a22a31a32|Adjoint of...
Practice Problem Set for Matrices and Absolute Values Symmetric Matrix Definition, Diagonalization & Examples Finding the Inverse of a 3x3 Matrix | Overview & Formula Inverse Matrix Formula & Examples Inverse Matrix | Definition, Example & Properties Determinant of a 3x3 Matrix | Formula, Calculation ...
Compute the determinant of this submatrix. You have found the(i, j)-minorofA. Determine thesign factor(-1)i+j. Multiply the(i, j)-minor ofAby the sign factor. The result is exactly the(i, j)-cofactorofA! Repeat Steps 1-4 for alli,j = 1,...,n. ...
Learn about cofactor of a matrix, formula to find the cofactor of a particular element, minors and cofactors along with the solved examples here at BYJU'S.
Keep in mind that cofactor expansion is a recursive formula. For instance, the determinant of a 5×5 matrix with cofactor expansion is expressed via several 4×4 determinants. To see how to compute them, use the cofactor expansion calculator once again. Example: the determinant of a 5×5 ma...
P. The cumulative electrostatic effect of aromatic stacking interactions and the negative electrostatic environment of the flavin mononucleotide binding site is a major determinant of the reduction potential for the flavodoxin from Desulfovibrio vulgaris [Hildenborough]. Biochemistry 35, 15980–15988 (1996)...
This process is straightforward for m = 3 as the interim determinants are easily obtained from Eq. (10.23). However, for m = 4, the interim determinants are more difficult to obtain. In fact, one needs to apply the full Laplace expansion method to obtain the determinant of each interim 3...