logo

Ask Questions, Get Answers

X
 
Home  >>  CBSE XII  >>  Math  >>  Matrices

$ (i)$ Show that the matrix $A = \begin{bmatrix} 1 & -1 & 5 \\ -1 & 2 & 1 \\ 5 & 1 & 3 \end{bmatrix}$ is a symmetric matrix.

This question has multiple parts. Therefore each part has been answered as a separate question on Clay6.com
Download clay6 mobile app

1 Answer

Toolbox:
  • A square matrix A=[a$_{ij}$] is said to be symmetric if A'=A that is $[a_{ij}]=[a_{ji}]$ for all possible value of i and j.
$(i)Given A = \begin{bmatrix} 1 & -1 & 5 \\ -1 & 2 & 1 \\ 5 & 1 & 3 \end{bmatrix} $
$a_{21}=a_{12}=-1$
$a_{31}=a_{13}=5$
$a_{32}=a_{23}=1$
$a_{11}=a_{22}=a_{33}$ are 1 2 3 respectively.
Hence $a_{ij}=a_{ji}$
Therefore A is a symmetric matrix.
$ A '= \begin{bmatrix} 1 & -1 & 5 \\ -1 & 2 & 1 \\ 5 & 1 & 3 \end{bmatrix}=A $
Thus A is a symmetric matrix.
answered Mar 14, 2013 by sharmaaparna1
 

Related questions

Ask Question
Tag:MathPhyChemBioOther
...
X