Ask Questions, Get Answers

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

If \( A = \begin{bmatrix} 6 & -5 \\ 2 & 3 \end{bmatrix} \), then show that A-A' is skew matrix.

Can you answer this question?

1 Answer

0 votes
  • If A_{i,j} be a matrix m*n matrix , then the matrix obtained by interchanging the rows and column of A is called as transpose of A.
  • 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.
  • The sum / difference $A(+/-)B$ of two $m$-by-$n$ matrices $A$ and $B$ is calculated entrywise: $(A (+/-) B)_{i,j} = A_{i,j} +/- B_{i,j}$ where 1 ≤ i ≤ m and 1 ≤ j ≤ n.
  • From the property of the skew symmetric matrix we have the diagonal of the matrix to be zero.
$A=\begin{bmatrix}6 &-5\\2 & 3\end{bmatrix}$
Transpose can be obtained by changing the rows and column.
$A'=\begin{bmatrix}6 &2\\-5 & 3\end{bmatrix}$
A-A'=$\begin{bmatrix}6 &-5\\2 & 3\end{bmatrix}+(-1)\begin{bmatrix}6 &2\\-5& 3\end{bmatrix}$
$\;\;\;=\begin{bmatrix}6 &-5\\2 & 3\end{bmatrix}+\begin{bmatrix}-6 &-2\\5& -3\end{bmatrix}$
$\;\;\;=\begin{bmatrix}0 & -7\\7 & 0\end{bmatrix}$
Since the diagonal of the matrix is zero,we can say that A-A'-skew symmetric matrix.
answered Apr 10, 2013 by sharmaaparna1

Related questions

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