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Created page with "<div style="font-size:30px">'''MATRIXADJOINT (a)'''</div><br/> *<math>a</math> is any set of values. ==Description== *This function shows the Adjoint of a given matrix. *In <..."
<div style="font-size:30px">'''MATRIXADJOINT (a)'''</div><br/>
*<math>a</math> is any set of values.
==Description==
*This function shows the Adjoint of a given matrix.
*In <math>MATRIXADJOINT (a)</math>,<math>a</math> 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 <math>adj A</math>.
*The adjugate of A is the transpose of the cofactor matrix C of A, <math>adj(A)= C^T</math>.
*Also adjoint of a matrix is defined by <math>adj(A)= det(A).A^{-1}</math>.
*The adjugate of 1x1 matrix is <math>I=(1)</math>.
*The adjugate of 2x2 matrix <math>:A=
\begin{pmatrix}
a & b \\
c & d
\end{pmatrix} </math>is <math>adj(A)=\begin{pmatrix}
d & -b \\
-c & a
\end{pmatrix}</math>.
*Consider3x3 matrix <math>A=\begin{pmatrix}
a_{11} & a_{12} & a_{13} \\
a_{21} & a_{22} & a_{23} \\
a_{31} & a_{32} & a_{33}
\end{pmatrix} </math>.
*Its adjugate is the transpose of its cofactor matrix:<math>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}</math>
*<math>a</math> is any set of values.
==Description==
*This function shows the Adjoint of a given matrix.
*In <math>MATRIXADJOINT (a)</math>,<math>a</math> 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 <math>adj A</math>.
*The adjugate of A is the transpose of the cofactor matrix C of A, <math>adj(A)= C^T</math>.
*Also adjoint of a matrix is defined by <math>adj(A)= det(A).A^{-1}</math>.
*The adjugate of 1x1 matrix is <math>I=(1)</math>.
*The adjugate of 2x2 matrix <math>:A=
\begin{pmatrix}
a & b \\
c & d
\end{pmatrix} </math>is <math>adj(A)=\begin{pmatrix}
d & -b \\
-c & a
\end{pmatrix}</math>.
*Consider3x3 matrix <math>A=\begin{pmatrix}
a_{11} & a_{12} & a_{13} \\
a_{21} & a_{22} & a_{23} \\
a_{31} & a_{32} & a_{33}
\end{pmatrix} </math>.
*Its adjugate is the transpose of its cofactor matrix:<math>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}</math>