Question:
The matrix $\left[\begin{array}{rrr}0 & 5 & -7 \\ -5 & 0 & 11 \\ 7 & -11 & 0\end{array}\right]$ is
(a) a skew-symmetric matrix
(b) a symmetric matrix
(c) a diagonal matrix
(d) an uppertriangular matrix
Solution:
(a) a skew-symmetric matrix
Here,
$A=\left[\begin{array}{ccc}0 & 5 & -7 \\ -5 & 0 & 11 \\ 7 & -11 & 0\end{array}\right]$
$\Rightarrow A^{T}=\left[\begin{array}{ccc}0 & -5 & 7 \\ 5 & 0 & -11 \\ -7 & 11 & 0\end{array}\right]$
$\Rightarrow A^{T}=-\left[\begin{array}{ccc}0 & 5 & -7 \\ -5 & 0 & 11 \\ 7 & -11 & 0\end{array}\right]$
$\Rightarrow A^{T}=-A$
Thus, $A$ is a skew-symmetric matrix.
Click here to get exam-ready with eSaral
For making your preparation journey smoother of JEE, NEET and Class 8 to 10, grab our app now.