Out of the following,a skew-symmetric matrix | vedclass

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(A) matrix $A$ is skew-symmetric if $A^T = -A$,which implies $a_{ij} = -a_{ji}$ for all $i, j$.For diagonal elements where $i = j$,we have $a_{ii} = -

Vedclass · Accepted Answer

$\begin{bmatrix} 0 & 4 & 5 \ -4 & 0 & -6 \ -5 & 6 & 0 \end{bmatrix}$

Vedclass · Answer

(A) matrix $A$ is skew-symmetric if $A^T = -A$,which implies $a_{ij} = -a_{ji}$ for all $i, j$.For diagonal elements where $i = j$,we have $a_{ii} = -a_{ii}$,which implies $2a_{ii} = 0$,so $a_{ii} = 0$.Checking option $A$:Let $A = \begin{bmatrix} 0 & 4 & 5 \ -4 & 0 & -6 \ -5 & 6 & 0 \end{bmatrix}$.$A^T = \begin{bmatrix} 0 & -4 & -5 \ 4 & 0 & 6 \ 5 & -6 & 0 \end{bmatrix} = -\begin{bmatrix} 0 & 4 & 5 \ -4 & 0 & -6 \ -5 & 6 & 0 \end{bmatrix} = -A$.Since $A^T = -A$,the matrix is skew-symmetric.

Out of the following,a skew-symmetric matrix is:

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