用定义证明矩阵线性空间 $M _{2 \times 2}( R )$ 中四个元素：

$$
E _{11}=\left[\begin{array}{ll}
1 & 0 \\
0 & 0
\end{array}\right], E _{12}=\left[\begin{array}{ll}
0 & 1 \\
0 & 0
\end{array}\right], E _{21}=\left[\begin{array}{ll}
0 & 0 \\
1 & 0
\end{array}\right], E _{22}=\left[\begin{array}{ll}
0 & 0 \\
0 & 1
\end{array}\right]
$$


线性无关。