\[\text {span}\left \{\begin{bmatrix}1 & 0 & 0\\0 & 0 & 0\\0 & 0 & 0\end{bmatrix},\begin{bmatrix}0 & 0 & 0\\0 & 1 & 0\\0 & 0 & 0\end{bmatrix}, \begin{bmatrix}0 & 0 & 0\\0 & 0 & 0\\0 & 0 & 1\end{bmatrix}, \begin{bmatrix}0 & 1 & 0\\1 & 0 & 0\\0 & 0 & 0\end{bmatrix}, \begin{bmatrix}0 & 0 & 1\\0 & 0 & 0\\1 & 0 & 0\end{bmatrix}, \begin{bmatrix}0 & 0 & 0\\0 & 0 & 1\\0 & 1 & 0\end{bmatrix}\right \}\]
The subspace consists of:
Matrices \(A\) of \(\mathbb {M}_{3,3}\) such that \(A^T=A\). All invertible matrices of \(\mathbb {M}_{3,3}\). Upper and lower triangular matrices of \(\mathbb {M}_{3,3}\). All of \(\mathbb {M}_{3,3}\).