# Difference between revisions of "Manuals/calci/ADJ"

Jump to navigation
Jump to search

Line 56: | Line 56: | ||

\end{vmatrix} \\ | \end{vmatrix} \\ | ||

\end{pmatrix}</math> | \end{pmatrix}</math> | ||

− | + | ||

− | + | ==Examples== | |

− | + | 1.adj([[10,12],[-14,21]]) | |

− | + | {| class="wikitable" | |

+ | |+Spreadsheet | ||

+ | |- | ||

+ | | 21 ||-12 | ||

+ | |- | ||

+ | |14 || 10 | ||

+ | |} | ||

+ | 2.adj([[4,5,8],[3,-6,-9],[10,-12,4]]) | ||

+ | {| class="wikitable" | ||

+ | |+Spreadsheet | ||

+ | |- | ||

+ | | -132 ||-116||2.9999999999999982 | ||

+ | |- | ||

+ | | -102|| -64|| 60 | ||

+ | |- | ||

+ | | 24 || 98 || -39 | ||

+ | |} | ||

+ | |||

+ | 3.adj([[5,-2,2,7],[1,0,0,3], [-3,1,5,0], [3,-1,-9,4]]) | ||

+ | {| class="wikitable" | ||

+ | |+Spreadsheet | ||

+ | |- | ||

+ | | -12 ||76||-60 ||-36 | ||

+ | |- | ||

+ | | -56 || 207.99999999999997 || -81.99999999999999 || -57.99999999999999 || | ||

+ | |- | ||

+ | | 4 || 3.999999999999999 || -1.9999999999999998 || -10 || | ||

+ | |- | ||

+ | | 4 ||3.9999999999999982 || 20 || 12 || | ||

+ | |} | ||

+ | |||

+ | ==See Also== | ||

+ | *[[Manuals/calci/MATRIXADJOINT | MATRIXADJOINT ]] | ||

+ | *[[Manuals/calci/MINVERSE | MINVERSE ]] | ||

+ | *[[Manuals/calci/MMULT | MMULT ]] | ||

==References== | ==References== | ||

*[https://en.wikipedia.org/wiki/Adjugate_matrix Adjugate matrix] | *[https://en.wikipedia.org/wiki/Adjugate_matrix Adjugate matrix] |

## Revision as of 15:05, 1 June 2017

**ADJ(Array)**

- is the set of values.

## Description

- This function shows the Adjoint of a given matrix.
- In , is the set of matrix values.
- Adjoint of a matrix is called adjugate, classical adjoint, or adjunct.Adjoint of a matrix formed by taking the transpose of the cofactor matrix of a given original Square matrix.
- Adjoint of matrix A is written by .
- The adjugate of A is the transpose of the cofactor matrix C of A, .
- Also adjoint of a matrix is defined by .
- The adjugate of 1x1 matrix is .
- The adjugate of 2x2 matrix is .
- Consider3x3 matrix .
- Its adjugate is the transpose of its cofactor matrix:

## Examples

1.adj([[10,12],[-14,21]])

21 | -12 |

14 | 10 |

2.adj([[4,5,8],[3,-6,-9],[10,-12,4]])

-132 | -116 | 2.9999999999999982 |

-102 | -64 | 60 |

24 | 98 | -39 |

3.adj([[5,-2,2,7],[1,0,0,3], [-3,1,5,0], [3,-1,-9,4]])

-12 | 76 | -60 | -36 | |

-56 | 207.99999999999997 | -81.99999999999999 | -57.99999999999999 | |

4 | 3.999999999999999 | -1.9999999999999998 | -10 | |

4 | 3.9999999999999982 | 20 | 12 |