Examples | |
---|---|

- | Ex: $2 \times 2$ matrix |

- | Ex: $3 \times 3$ matrix |

- | Ex: $4 \times 4$ matrix |

General | |
---|---|

- | Definition |

Example: $2 \times 2$ matrix

Let $A$ be a $2 \times 2$ matrix defined as
Let $M_{ij}$ be a submatrix given by removing $i$-th row and $j$-th column from $A$,

Example

Let $A$ be a $2 \times 2$ matrix given as
Calculator

Enter a $2 \times 2$ matrix and press "Execute" button.
Its cofactor matrix is displayed.
Matrix $A$

1 | 2 | |

1 | ||

2 |

Example: $3 \times 3$ matrix

Let $A$ be a $3 \times 3$ matrix given as
Let $M_{ij}$ be a submatrix given by removing $i$-th row and $j$-th column from $A$,

Let $A$ be a 3x3 matrix given as

Calculator

Enter a $3 \times 3$ matrix and press "Execute" button.
Its cofactor matrix is displayed.
Example: $4 \times 4$ matrix

Find the cofactor matrix of
Let $M_{ij}$ be a submatrix given by removing $i$-th row and $j$-th column from $A$,

Calculator

Enter a $4 \times 4$ matrix and press "Execute" button.
Its cofactor matrix is displayed.
Definition of cofactor matrix

Let $a_{ij}$ be the $i$-th row and $j$-th column element of an $n \times n$ matrix $A$,
and $M_{ij}$ be the sub-matrix obtained by removing the $i$-th row and $j$-column: