Symmetric and Skew-Symmetric Matrices Exercise (with Solution)

Exercise

\[\] \[ \begin{array}{|c|c|} \hline \textbf{Matrix} & \textbf{Symmetric or Skew-Symmetric?} \\ \hline \begin{pmatrix} 1 & 2 \\ 2 & 1 \end{pmatrix} & ? \\ \hline \begin{pmatrix} 0 & -1 \\ 1 & 0 \end{pmatrix} & ? \\ \hline \begin{pmatrix} 3 & 4 & 5 \\ 4 & 6 & 7 \\ 5 & 7 & 8 \end{pmatrix} & ? \\ \hline \begin{pmatrix} 1 & 2 & 3 \\ -2 & 4 & 5 \\ -3 & -5 & 6 \end{pmatrix} & ? \\ \hline \begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix} & ? \\ \hline \begin{pmatrix} 2 & 1 \\ -1 & -2 \end{pmatrix} & ? \\ \hline \end{array} \]

Solution:

\[\] \[ \begin{array}{|c|c|} \hline \textbf{Matrix} & \textbf{Symmetric or Skew-Symmetric?} \\ \hline \begin{pmatrix} 1 & 2 \\ 2 & 1 \end{pmatrix} & \text{Symmetric} \\ \hline \begin{pmatrix} 0 & -1 \\ 1 & 0 \end{pmatrix} & \text{Skew-Symmetric} \\ \hline \begin{pmatrix} 3 & 4 & 5 \\ 4 & 6 & 7 \\ 5 & 7 & 8 \end{pmatrix} & \text{Symmetric} \\ \hline \begin{pmatrix} 1 & 2 & 3 \\ -2 & 4 & 5 \\ -3 & -5 & 6 \end{pmatrix} & \text{Skew-Symmetric} \\ \hline \begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix} & \text{Symmetric} \\ \hline \begin{pmatrix} 2 & 1 \\ -1 & -2 \end{pmatrix} & \text{Skew-Symmetric} \\ \hline \end{array} \]

Leave a Comment

All Copyrights Reserved 2025 Reserved by T4Tutorials