>The following matrix over $\mathbb{Z_5}$ is given:
$$
\begin{bmatrix}
2 & 2& 2& 3\\
1&3&1&3\\
3&0&2&2\\
4&1&0&4\\
1&2&2&0
\end{bmatrix}
$$
Specify the dimension of the row space and the column space.
Specify a base BS for the row space and a base BS for the column space.
Row-space:
$$
\begin{bmatrix}
2 & 2& 2& 3\\
1&3&1&3\\
3&0&2&2\\
4&1&0&4\\
1&2&2&0
\end{bmatrix}
\iff
\begin{bmatrix}
2 & 2& 2& 3\\
0&2&0&4\\
0&0&4&1\\
0&0&0&0\\
0&0&0&0
\end{bmatrix}
\implies \dim(Row)=3
$$
Now a question: Is