Question

The matrix \[\left[{\begin{array}{*{20}{c}}0&5&{ - 7}\\{ - 5}&0&{11}\\7&{ -11}&0\end{array}} \right]\] is known as
A. Upper Triangular Matrix
B. Skew Symmetric Matrix
C. Symmetric matrix
D. Diagonal Matrix

Answer 1

Hint:
Firstly we are given a matrix A and we have to find its transpose and then after finding the transpose we will see that it will be equal to its negative of the given matrix and we will get our required solution.


Formula Used:

For skew-symmetric matrix,
\[{A^T}= - A\]


Complete Step-by-Step Solution:

A skew-symmetric matrix is a square matrix that is equal to the negative of its transpose matrix.
It is important to know the method to find the transpose of a matrix, in order to understand a
skew-symmetric matrix better. Here, we have considered a matrix A.
The basic formula representing a Skew Symmetric Matrix is as follows.
\[A = - {A^T}\]
Given matrix, \[A =\] \[\left[ {\begin{array}{*{20}{c}}0&5&{ - 7}\\{- 5}&0&{11}\\7&{ - 11}&0\end{array}} \right]\]
Now, we will find its transpose.
\[{A^T} =\left[ {\begin{array}{*{20}{c}}0&{-5}&{ 7}\\{ 5}&0&{-11}\\{-7}&{ 11}&0\end{array}} \right]\]
Here, \[{A^T}= - A\].
Hence it follows the definition of the skew-symmetric matrix.
Option B is correct.

Note:
Students should always remember the definitions of such matrices as in such questions it will be very helpful to them. And whenever such a question comes, we can transpose the matrix and then in the next step we will see which type of matrix it will become.