Manuals/calci/ADJ

ADJ(Array)

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle Array} is the set of values.

Description

This function shows the Adjoint of a given matrix.
In Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle ADJ(Array)} ,Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle Array} 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 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle adj A} .
The adjugate of A is the transpose of the cofactor matrix C of A, Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle adj(A)= C^T} .
Also adjoint of a matrix is defined by Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle adj(A)= det(A).A^{-1}} .
The adjugate of 1x1 matrix is $I=(1)$ .
The adjugate of 2x2 matrix Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle :A= \begin{pmatrix} a & b \\ c & d \end{pmatrix} } is Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle adj(A)=\begin{pmatrix} d & -b \\ -c & a \end{pmatrix}} .
Consider3x3 matrix Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle A=\begin{pmatrix} a_{11} & a_{12} & a_{13} \\ a_{21} & a_{22} & a_{23} \\ a_{31} & a_{32} & a_{33} \end{pmatrix} } .
Its adjugate is the transpose of its cofactor matrix:Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle adj(A)=C^{T} = \begin{pmatrix} +\begin{vmatrix} a_ {22}& a_{23} \\ a_ {32}& a_{33} \end{vmatrix} & - \begin{vmatrix} a_ {12}& a_{13} \\ a_ {32}& a_{33} \end{vmatrix} & +\begin{vmatrix} a_ {12}& a_{13} \\ a_ {22}& a_{23} \end{vmatrix} \\ +\begin{vmatrix} a_ {21}& a_{23} \\ a_ {31}& a_{33} \end{vmatrix} & - \begin{vmatrix} a_ {11}& a_{13} \\ a_ {31}& a_{33} \end{vmatrix} & +\begin{vmatrix} a_ {11}& a_{13} \\ a_ {21}& a_{23} \end{vmatrix} \\ +\begin{vmatrix} a_ {21}& a_{22} \\ a_ {31}& a_{32} \end{vmatrix} & - \begin{vmatrix} a_ {11}& a_{12} \\ a_ {31}& a_{32} \end{vmatrix} & +\begin{vmatrix} a_ {11}& a_{12} \\ a_ {21}& a_{22} \end{vmatrix} \\ \end{pmatrix}}