logo

Ask Questions, Get Answers

 
X
 Search
Want to ask us a question? Click here
Browse Questions
Ad
Home  >>  CBSE XII  >>  Math  >>  Model Papers
0 votes

Show that elements on the main diagonal of a skew-symmetric matrix are all zero.

Can you answer this question?
 
 

1 Answer

0 votes
Toolbox:
  • A square matrix A=[a$_{ij}$] is said to be skew symmetric if A'=-A that is $[a_{ij}]= -[a_{ji}]$ for all possible value of i and j.
To prove:
All diagonal elements of a skew-symmetric matrix are all zero.
Proof:
Let $A=[a_{ij}]_{n\times n}$ be a skew symmetric matrix.
$\Rightarrow a_{ij}=-a_{ji}$ for all i & j.
$\Rightarrow a_{ii}=-a_{ii}$ $\quad (Put \;j=i)$
$\Rightarrow 2a_{ii}=0\Rightarrow a_{ii}=0.$
Thus in a skew symmetric matrix all elements along the principal diagonal are zero.
answered Apr 11, 2013 by sharmaaparna1
 

Related questions

Ask Question
student study plans
x
JEE MAIN, CBSE, NEET Mobile and Tablet App
The ultimate mobile app to help you crack your examinations
Get the Android App
...