Question

Determine which of the matrices in Exercises 1–6 are symmetric.

4. \(\left( {\begin{aligned}{{}}0&8&3\\8&0&{ - 4}\\3&2&0\end{aligned}} \right)\)

Short answer

The given matrix is not symmetric.

Step-by-step solution

Find the transpose

A matrix\(A\) with, \(n \times n\) dimension, is symmetric if it satisfies the equation\({A^T} = A\).

It is given that\(A = \left( {\begin{aligned}{{}}0&8&3\\8&0&{ - 4}\\3&2&0\end{aligned}} \right)\). Find the transpose of\(A\), as shown below:

\(\begin{aligned}{}{A^T} = \left( {\begin{aligned}{{}}0&8&3\\8&0&2\\3&{ - 4}&0\end{aligned}} \right)\\ \ne A\end{aligned}\)

Draw the conclusion

As \({A^T} \ne A\), so it can be concluded that \(A\) is not asymmetric matrix.