If A is symmetric and B is skew symmetric matrix and $A+B=\begin{bmatrix} 1 & -1\\3 & 2\end{bmatrix}$, then matrix A = _______.
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → $\begin{bmatrix} 1 & 1\\1 & 2\end{bmatrix}$
$A=\begin{bmatrix} a & c\\c & d\end{bmatrix},B=\begin{bmatrix} 0 & x\\-x & 0\end{bmatrix}$
$A+B=\begin{bmatrix} a+0 & c+x\\c-x & d+0\end{bmatrix}=\begin{bmatrix} 1 & -1\\3 & 2\end{bmatrix}$
$a=1,c+x=3,d=2,c-x=-1$
$c+x=3$ ...(1)
$c-x=-1$ ...(2)
from (1) and (2)
$2c=2$
$c=1,x=2$
$A=\begin{bmatrix} 1 & 1\\1 & 2\end{bmatrix}$