Changes

==Description==

==Description==

*This function returns the symmetric matrix of order 3.

*This function returns the symmetric matrix of order 3.

*A symmetric matrix is a square matrix that satisfies <math>A^(T)=A</math>,where <math>A^(T)</math> denotes the transpose.  

*A symmetric matrix is a square matrix that satisfies <math>A^T=A</math>,where <math>A^T</math> denotes the transpose.  

*i.e., A square matrix which is equal to its transpose is called symmetric matrix.  

*i.e., A square matrix which is equal to its transpose is called symmetric matrix.  

*So <math>a_(ij)=a_(ji)</math>.  

*So <math>a_{ij}=a_{ji}</math>.  

*This also implies <math>A^(-1)A^(T)=I</math>,  where I is the identity matrix.

*This also implies <math>A^{-1}A^T=I</math>,  where I is the identity matrix.

*Because equal matrices have equal dimensions, only square matrices can be symmetric.  

*Because equal matrices have equal dimensions, only square matrices can be symmetric.  

*An example for the symmetric matrix is   

*An example for the symmetric matrix is   

-5 & -11 & -75 \\

-5 & -11 & -75 \\

-93 & -75 & -7 \\  

-93 & -75 & -7 \\  

\end{pmatrix}  

\end{pmatrix} </math>

*The properties of symmetric matrices are:

*The properties of symmetric matrices are:

*1.Every square diagonal matrix is symmetric, since all off-diagonal entries are zero.  

*1.Every square diagonal matrix is symmetric, since all off-diagonal entries are zero.