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Cofactor matrix is the matrix containing the cofactors of each of the elements of the given matrix. Here we shall learn how to find the cofactor matrix, the formula for cofactor, application of cofactor matrix, and solved examples.
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.
Cofactor matrix is the matrix formed by the Cofactor of each element of any matrix where cofactor is a number that is obtained by multiplying the minor of the element of any given matrix with -1 raised to the power of the sum of the row and column number to which that element belongs.
To find the cofactor matrix, compute the cofactor of each element in the matrix and replace each element by its cofactor. Once we’ve seen the definition of cofactor matrix, let’s see two examples of how to compute the cofactor matrix.
In this section, we give a recursive formula for the determinant of a matrix, called a cofactor expansion. The formula is recursive in that we will compute the determinant of an n × n matrix assuming we already know how to compute the determinant of an (n − 1) × (n − 1) matrix.
Discover how to find cofactors of any matrix with our user-friendly cofactor matrix calculator. Simplify matrix operations effortlessly!
Cofactor formula The cofactor formula rewrites the big formula for the determinant of an n by n matrix in terms of the determinants of smaller matrices. 2
Given a factor a of a number n=ab, the cofactor of a is b=n/a. A different type of cofactor, sometimes called a cofactor matrix, is a signed version of a minor M_ (ij) defined by C_ (ij)= (-1)^ (i+j)M_ (ij) and used in the computation of the determinant of a matrix A according to |A|=sum_ (i=1)^ka_ (ij)C_ (ij).
The cofactor of an element of a matrix is its minor multiplied by -1 raised to the sum of its row number and column number. Understand the cofactor formula using examples.
Inverse of a Matrix. using Minors, Cofactors and Adjugate. Note: also check out Matrix Inverse by Row Operations and the Matrix Calculator. We can calculate the Inverse of a Matrix by: Step 1: calculating the Matrix of Minors, Step 2: then turn that into the Matrix of Cofactors, Step 3: then the Adjugate, and.