数学试题讲解

用定义证明矩阵线性空间

M_{2 \times 2} (R)

中四个元素：

E_{11} = [\begin{array}{ll} 1 & 0 \\ 0 & 0 \end{array}], E_{12} = [\begin{array}{ll} 0 & 1 \\ 0 & 0 \end{array}], E_{21} = [\begin{array}{ll} 0 & 0 \\ 1 & 0 \end{array}], E_{22} = [\begin{array}{ll} 0 & 0 \\ 0 & 1 \end{array}]

线性无关。