Question

The symmetric part of the matrix $\left[\begin{array}{ccc}2& 1& 3\\ 1& 1& 4\\ -1& 6& 2\end{array}\right]$ is

• A. $\left[\begin{array}{ccc}0& 0& 2\\ 0& 0& -1\\ -2& 1& 0\end{array}\right]$
• B. $\left[\begin{array}{ccc}2& 1& 1\\ 1& 1& 5\\ 1& 5& 2\end{array}\right]$
• C. $\left[\begin{array}{ccc}0& 0& -2\\ 0& 0& 1\\ 2& 1& 0\end{array}\right]$
• D. $\left[\begin{array}{ccc}2& 1& 1\\ 1& 1& 6\\ 3& 4& 2\end{array}\right]$

Answer 1

The correct option is B $\left[\begin{array}{ccc}2& 1& 1\\ 1& 1& 5\\ 1& 5& 2\end{array}\right]$

Symmetric point of the matrix A' is $\frac{1}{2}(A+A^T)$
$i.e\frac{1}{2}$ $\left[\begin{array}{ccc}4& 2& 2\\ 2& 2& 10\\ 2& 10& 4\end{array}\right]=\left[\begin{array}{ccc}2& 1& 1\\ 1& 1& 5\\ 1& 5& 2\end{array}\right]$