Cofactor Matrix Calculator

Enter a 3x3 Matrix

 Cofactor Matrix Calculator Example

To explain how the cofactor matrix calculator works, let's consider the following example:

Example: Find the cofactor matrix of matrix A:

A = | 2 -3 5 |

      | 6 0 1 |

       | 1 5 -7 |

Step 1: Define the Cofactor Formula

The cofactor Cij of an element aij in matrix A is calculated as:

Cij = (-1)^(i+j) * Mji

Where:

i and j are the row and column indices of element aij, respectively.

(-1)^(i+j) is the sign factor, which is 1 if the sum of i and j is even and -1 if the sum is odd.

MG is the determinant of the minor matrix obtained by removing the ith row and jth column of A.

Step 2: Calculate Coefficients

Cofactor of A11:

i = 1, j = 1

(-1)^(i+j) = (-1)^(1+1) = 1

M11 = | 0 1 | = 1

C11 = 1 * 1 = 1

Cofactor of A12:

i = 1, j = 2

(-1)^(i+j) = (-1)^(1+2) = -1

M12 = | 1 -7 | = -8

C12 = -1 * (-8) = 8

Calculate the remaining cofactors in the same way using the formula.

Step 3: Construct the Cofactor Matrix

The cofactor matrix is constructed by placing the cofactors in their corresponding positions.

Cofactor matrix = | 1 8 -24 |

                     | 14 -329 |

                     | -23 31 6 |

Therefore, the cofactor matrix of matrix A is:

| 1 8 -24 |

| 14 -329 |

| -23 31 6 |