Question

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

1. \(\left[ {\begin{aligned}{{}}3&{\,\,\,5}\\5&{ - 7}\end{aligned}} \right]\)

Short answer

The given matrix is 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\(A = \left[ {\begin{aligned}{{}}3&{\,\,5}\\5&{ - 7}\end{aligned}} \right]\). Find the transpose of\(A\), as shown below:

\(\begin{aligned}{}{A^T} &= \left[ {\begin{aligned}{{}}3&{\,\,5}\\5&{ - 7}\end{aligned}} \right]\\ &= A\end{aligned}\)

Draw the conclusion

As \({A^T} = A\), so it can be concluded that \(A\) is a symmetric matrix.