Login/Sign Up
Find $1 / 2\left(A+A^{\prime}\right)$ and $1 / 2\left(A-A^{\prime}\right)$ when $A$ is $\left[\begin{array}{ccc}0 & a & b \\ -a & 0 & c \\ -b & -c & 0\end{array}\right]$
Find $1 / 2\left(A+A^{\prime}\right)$ and $1 / 2\left(A-A^{\prime}\right)$ when $A$ is $\left[\begin{array}{ccc}0 & a & b \\ -a & 0 & c \\ -b & -c & 0\end{array}\right]$
CBSE | Class 12 | Exercise 3.3 | Maths | Matrices | NCERT
Find $1 / 2\left(A+A^{\prime}\right)$ and $1 / 2\left(A-A^{\prime}\right)$ when $A$ is $\left[\begin{array}{ccc}0 & a & b \\ -a & 0 & c \\ -b & -c & 0\end{array}\right]$

$A=\left[\begin{array}{ccc}0 & a & b \\ -a & 0 & c \\ -b & -c & 0\end{array}\right]$ then $A^{\prime}=\left[\begin{array}{ccc}0 & -a & -b \\ a & 0 & -c \\ b & c & 0\end{array}\right]$
as, $A+A^{\prime}$ is

$\left[\begin{array}{ccc}0 & a & b \\ -a & 0 & c \\ -b & -c & 0\end{array}\right]+\left[\begin{array}{ccc}0 & -a & -b \\ a & 0 & -c \\ b & c & 0\end{array}\right]=\left[\begin{array}{lll}0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{array}\right]$

$So,1 / 2\left(A+A^{\prime}\right)$ is

$\frac{1}{2}\left[\begin{array}{lll}0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{array}\right]=\left[\begin{array}{lll}0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{array}\right]$

$A-A^{\prime}=\left[\begin{array}{ccc}0 & a & b \\ -a & 0 & c \\ -b & -c & 0\end{array}\right]-\left[\begin{array}{ccc}0 & -a & -b \\ a & 0 & -c \\ b & c & 0\end{array}\right]=\left[\begin{array}{ccc}0 & 2 a & 2 b \\ -2 a & 0 & 2 c \\ -2 b & -2 c & 0\end{array}\right]$

$1 / 2\left(A-A^{\prime}\right)=1 / 2\left[\begin{array}{ccc}0 & 2 a & 2 b \\ -2 a & 0 & 2 c \\ -2 b & -2 c & 0\end{array}\right]=\left[\begin{array}{rrr}0 & a & b \\ -a & 0 & c \\ -b & -c & 0\end{array}\right]$

i

More Material