Q. 66 On using elementary column operations $C_2 \rightarrow C_2-2 C_1$ in the following matrix equation $\left[\begin{array}{cc}1 & -3 \\ 2 & 4\end{array}\right]=\left[\begin{array}{cc}1 & -1 \\ 0 & 1\end{array}\right]\left[\begin{array}{ll}3 & 1 \\ 2 & 4\end{array}\right]$, we have
On using elementary row operation $R_1 \rightarrow R_1-3 R_2$ in the following matrix equation $\left[\begin{array}{ll}4 & 2 \\ 3 & 3\end{array}\right]=\left[\begin{array}{ll}1 & 2 \\ 0 & 3\end{array}\right]\left[\begin{array}{ll}2 & 0 \\ 1 & 1\end{array}\right]$, we have
........... matrix is both symmetric and skew-symmetric matrix.
Null matrix is both symmetric and skew-symmetric matrix.
Sum of two skew-symmetric matrices is always ........... matrix.
Let $A$ is a given matrix, then $(-A)$ is a skew-symmetric matrix. Similarly, for a given matrix $-B$ is a skew-symmetric matrix. Hence, $-A-B=-(A+B) \Rightarrow$ sum of two skew-symmetric matrices is always skew-symmetric matrix.
The negative of a matrix is obtained by multiplying it by ............ .
Let $A$ is a given matrix.
$\therefore \quad-A=-1[A]$
So, the negative of a matrix is obtained by multiplying it by $-1$.