How To Find The Cofactors | The Science

 

 

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How to find the cofactors

Algebraic addition - an element of the matrix or linear algebra, one of the concepts of higher mathematics along with determinant minor and inverse matrix. However, despite the apparent complexity, it is not difficult to find algebraic additions.

How to find the cofactors

Instruction how to find the cofactors

Step 1:

Matrix algebra as a branch of mathematics is important for recording the mathematical models in a more compact form. For example, the concept of the determinant of a square matrix is ​​directly related to finding solutions of systems of linear equations, which are used in a variety of applications, including on the economy.

Step 2:

The algorithm for finding the cofactors matrix is ​​closely related to the concepts of the minor and the determinant of the matrix. The determinant of the matrix of the second order is calculated as follows: Δ = a11·a22 - a12·a21.

Step 3:

Minor element matrix of order n - is the determinant of the matrix of order (n-1), which is obtained by removing the row and column corresponding to the position of this element. For example, the minor of the matrix element, standing in the second row, third column: M23 = a11·a32 - a12·a31.

Step 4:

Algebraic addition of the matrix element - a minor element of the sign, which is directly dependent on what position an element takes in the matrix. In other words, the cofactor is equal to the minor, if the amount of row and column element - an even number, and opposite in sign, when this number - odd: Aij = (-1) ^ (i + j)·Mij.

Step 5:

Primer.Naydite cofactors for all elements of the matrix.

Step 6:

Reshenie.Ispolzuyte above formula to calculate cofactors. Be careful when determining the sign and write determinant of the matrix: A11 = M11 = a22·a33 - a23·a32 = (0 - 10) = -10; A12 = -M12 = - (a21·a33 - a23·a31) = - (3 - 8) = 5; A13 = M13 = a21·a32 - a22·a31 = (5 - 0) = 5;

Step 7:

A21 = -M21 = - (a12·a33 - a13·a32) = - (6 + 15) = -21; A22 = M22 = a11·a33 - a13·a31 = (3 + 12) = 15; A23 = -M23 = - (a11·a32 - a12·a31) = - (5 - 8) = 3;

Step 8:

A31 = M31 = a12·a23 - a13·a22 = (4 + 0) = 4; A32 = -M32 = - (a11·a23 - a13·a21) = - (3 + 2) = -5; A33 = M33 = a11·a22 - a12·a21 = (0 - 2) = -2.