求逆矩阵：
输入一个可逆矩阵，每个元用逗号隔开，每行用分号结尾。
注意，不支持支持数学函数和变量。
输入一个可逆矩阵，每个元用逗号隔开，每行用分号结尾。
注意，不支持支持数学函数和变量。
$$\begin{aligned}&\\ \color{black}{计算矩阵}& \ \ \begin{pmatrix} &4\ &3\ &3\ &3\ &3\ &3\ \\ &3\ &4\ &3\ &3\ &3\ &3\ \\ &3\ &3\ &4\ &3\ &3\ &3\ \\ &3\ &3\ &3\ &4\ &3\ &3\ \\ &3\ &3\ &3\ &3\ &4\ &3\ \\ &3\ &3\ &3\ &3\ &3\ &4\ \end{pmatrix}\color{black}{的逆矩阵。}\\ \\解:&\\ &\begin{pmatrix} &4\ &3\ &3\ &3\ &3\ &3\ \\ &3\ &4\ &3\ &3\ &3\ &3\ \\ &3\ &3\ &4\ &3\ &3\ &3\ \\ &3\ &3\ &3\ &4\ &3\ &3\ \\ &3\ &3\ &3\ &3\ &4\ &3\ \\ &3\ &3\ &3\ &3\ &3\ &4\ \end{pmatrix}\\\\&\color{grey}{用矩阵的初等变换来求逆矩阵：}\\&\left (\begin{array} {ccccccc | cccccc} &4\ &3\ &3\ &3\ &3\ &3\ &1\ &0\ &0\ &0\ &0\ &0\ \\ &3\ &4\ &3\ &3\ &3\ &3\ &0\ &1\ &0\ &0\ &0\ &0\ \\ &3\ &3\ &4\ &3\ &3\ &3\ &0\ &0\ &1\ &0\ &0\ &0\ \\ &3\ &3\ &3\ &4\ &3\ &3\ &0\ &0\ &0\ &1\ &0\ &0\ \\ &3\ &3\ &3\ &3\ &4\ &3\ &0\ &0\ &0\ &0\ &1\ &0\ \\ &3\ &3\ &3\ &3\ &3\ &4\ &0\ &0\ &0\ &0\ &0\ &1\ \\\end{array} \right )\\\\&\color{grey}{将已知矩阵化为上三角矩阵}\\\\->\ \ &\left (\begin{array} {ccccccc | cccccc} &4\ &3\ &3\ &3\ &3\ &3\ &1\ &0\ &0\ &0\ &0\ &0\ \\ &0\ &\frac{7}{4}\ &\frac{3}{4}\ &\frac{3}{4}\ &\frac{3}{4}\ &\frac{3}{4}\ &-\frac{3}{4}\ &1\ &0\ &0\ &0\ &0\ \\ &0\ &\frac{3}{4}\ &\frac{7}{4}\ &\frac{3}{4}\ &\frac{3}{4}\ &\frac{3}{4}\ &-\frac{3}{4}\ &0\ &1\ &0\ &0\ &0\ \\ &0\ &\frac{3}{4}\ &\frac{3}{4}\ &\frac{7}{4}\ &\frac{3}{4}\ &\frac{3}{4}\ &-\frac{3}{4}\ &0\ &0\ &1\ &0\ &0\ \\ &0\ &\frac{3}{4}\ &\frac{3}{4}\ &\frac{3}{4}\ &\frac{7}{4}\ &\frac{3}{4}\ &-\frac{3}{4}\ &0\ &0\ &0\ &1\ &0\ \\ &0\ &\frac{3}{4}\ &\frac{3}{4}\ &\frac{3}{4}\ &\frac{3}{4}\ &\frac{7}{4}\ &-\frac{3}{4}\ &0\ &0\ &0\ &0\ &1\ \\\end{array} \right )\\\\->\ \ &\left (\begin{array} {ccccccc | cccccc} &4\ &3\ &3\ &3\ &3\ &3\ &1\ &0\ &0\ &0\ &0\ &0\ \\ &0\ &\frac{7}{4}\ &\frac{3}{4}\ &\frac{3}{4}\ &\frac{3}{4}\ &\frac{3}{4}\ &-\frac{3}{4}\ &1\ &0\ &0\ &0\ &0\ \\ &0\ &0\ &\frac{10}{7}\ &\frac{3}{7}\ &\frac{3}{7}\ &\frac{3}{7}\ &-\frac{3}{7}\ &-\frac{3}{7}\ &1\ &0\ &0\ &0\ \\ &0\ &0\ &\frac{3}{7}\ &\frac{10}{7}\ &\frac{3}{7}\ &\frac{3}{7}\ &-\frac{3}{7}\ &-\frac{3}{7}\ &0\ &1\ &0\ &0\ \\ &0\ &0\ &\frac{3}{7}\ &\frac{3}{7}\ &\frac{10}{7}\ &\frac{3}{7}\ &-\frac{3}{7}\ &-\frac{3}{7}\ &0\ &0\ &1\ &0\ \\ &0\ &0\ &\frac{3}{7}\ &\frac{3}{7}\ &\frac{3}{7}\ &\frac{10}{7}\ &-\frac{3}{7}\ &-\frac{3}{7}\ &0\ &0\ &0\ &1\ \\\end{array} \right )\\\\->\ \ &\left (\begin{array} {ccccccc | cccccc} &4\ &3\ &3\ &3\ &3\ &3\ &1\ &0\ &0\ &0\ &0\ &0\ \\ &0\ &\frac{7}{4}\ &\frac{3}{4}\ &\frac{3}{4}\ &\frac{3}{4}\ &\frac{3}{4}\ &-\frac{3}{4}\ &1\ &0\ &0\ &0\ &0\ \\ &0\ &0\ &\frac{10}{7}\ &\frac{3}{7}\ &\frac{3}{7}\ &\frac{3}{7}\ &-\frac{3}{7}\ &-\frac{3}{7}\ &1\ &0\ &0\ &0\ \\ &0\ &0\ &0\ &\frac{13}{10}\ &\frac{3}{10}\ &\frac{3}{10}\ &-\frac{3}{10}\ &-\frac{3}{10}\ &-\frac{3}{10}\ &1\ &0\ &0\ \\ &0\ &0\ &0\ &\frac{3}{10}\ &\frac{13}{10}\ &\frac{3}{10}\ &-\frac{3}{10}\ &-\frac{3}{10}\ &-\frac{3}{10}\ &0\ &1\ &0\ \\ &0\ &0\ &0\ &\frac{3}{10}\ &\frac{3}{10}\ &\frac{13}{10}\ &-\frac{3}{10}\ &-\frac{3}{10}\ &-\frac{3}{10}\ &0\ &0\ &1\ \\\end{array} \right )\\\\->\ \ &\left (\begin{array} {ccccccc | cccccc} &4\ &3\ &3\ &3\ &3\ &3\ &1\ &0\ &0\ &0\ &0\ &0\ \\ &0\ &\frac{7}{4}\ &\frac{3}{4}\ &\frac{3}{4}\ &\frac{3}{4}\ &\frac{3}{4}\ &-\frac{3}{4}\ &1\ &0\ &0\ &0\ &0\ \\ &0\ &0\ &\frac{10}{7}\ &\frac{3}{7}\ &\frac{3}{7}\ &\frac{3}{7}\ &-\frac{3}{7}\ &-\frac{3}{7}\ &1\ &0\ &0\ &0\ \\ &0\ &0\ &0\ &\frac{13}{10}\ &\frac{3}{10}\ &\frac{3}{10}\ &-\frac{3}{10}\ &-\frac{3}{10}\ &-\frac{3}{10}\ &1\ &0\ &0\ \\ &0\ &0\ &0\ &0\ &\frac{16}{13}\ &\frac{3}{13}\ &-\frac{3}{13}\ &-\frac{3}{13}\ &-\frac{3}{13}\ &-\frac{3}{13}\ &1\ &0\ \\ &0\ &0\ &0\ &0\ &\frac{3}{13}\ &\frac{16}{13}\ &-\frac{3}{13}\ &-\frac{3}{13}\ &-\frac{3}{13}\ &-\frac{3}{13}\ &0\ &1\ \\\end{array} \right )\\\\->\ \ &\left (\begin{array} {ccccccc | cccccc} &4\ &3\ &3\ &3\ &3\ &3\ &1\ &0\ &0\ &0\ &0\ &0\ \\ &0\ &\frac{7}{4}\ &\frac{3}{4}\ &\frac{3}{4}\ &\frac{3}{4}\ &\frac{3}{4}\ &-\frac{3}{4}\ &1\ &0\ &0\ &0\ &0\ \\ &0\ &0\ &\frac{10}{7}\ &\frac{3}{7}\ &\frac{3}{7}\ &\frac{3}{7}\ &-\frac{3}{7}\ &-\frac{3}{7}\ &1\ &0\ &0\ &0\ \\ &0\ &0\ &0\ &\frac{13}{10}\ &\frac{3}{10}\ &\frac{3}{10}\ &-\frac{3}{10}\ &-\frac{3}{10}\ &-\frac{3}{10}\ &1\ &0\ &0\ \\ &0\ &0\ &0\ &0\ &\frac{16}{13}\ &\frac{3}{13}\ &-\frac{3}{13}\ &-\frac{3}{13}\ &-\frac{3}{13}\ &-\frac{3}{13}\ &1\ &0\ \\ &0\ &0\ &0\ &0\ &0\ &\frac{19}{16}\ &-\frac{3}{16}\ &-\frac{3}{16}\ &-\frac{3}{16}\ &-\frac{3}{16}\ &-\frac{3}{16}\ &1\ \\\end{array} \right )\\\\&\color{grey}{将对角线以上的元素化为0}\\\\->\ \ &\left (\begin{array} {ccccccc | cccccc} &4\ &3\ &3\ &3\ &3\ &0\ &\frac{28}{19}\ &\frac{9}{19}\ &\frac{9}{19}\ &\frac{9}{19}\ &\frac{9}{19}\ &-\frac{48}{19}\ \\ &0\ &\frac{7}{4}\ &\frac{3}{4}\ &\frac{3}{4}\ &\frac{3}{4}\ &0\ &-\frac{12}{19}\ &\frac{85}{76}\ &\frac{9}{76}\ &\frac{9}{76}\ &\frac{9}{76}\ &-\frac{12}{19}\ \\ &0\ &0\ &\frac{10}{7}\ &\frac{3}{7}\ &\frac{3}{7}\ &0\ &-\frac{48}{133}\ &-\frac{48}{133}\ &\frac{142}{133}\ &\frac{9}{133}\ &\frac{9}{133}\ &-\frac{48}{133}\ \\ &0\ &0\ &0\ &\frac{13}{10}\ &\frac{3}{10}\ &0\ &-\frac{24}{95}\ &-\frac{24}{95}\ &-\frac{24}{95}\ &\frac{199}{190}\ &\frac{9}{190}\ &-\frac{24}{95}\ \\ &0\ &0\ &0\ &0\ &\frac{16}{13}\ &0\ &-\frac{48}{247}\ &-\frac{48}{247}\ &-\frac{48}{247}\ &-\frac{48}{247}\ &\frac{256}{247}\ &-\frac{48}{247}\ \\ &0\ &0\ &0\ &0\ &0\ &\frac{19}{16}\ &-\frac{3}{16}\ &-\frac{3}{16}\ &-\frac{3}{16}\ &-\frac{3}{16}\ &-\frac{3}{16}\ &1\ \\\end{array} \right )\\\\->\ \ &\left (\begin{array} {ccccccc | cccccc} &4\ &3\ &3\ &3\ &0\ &0\ &\frac{37}{19}\ &\frac{18}{19}\ &\frac{18}{19}\ &\frac{18}{19}\ &-\frac{39}{19}\ &-\frac{39}{19}\ \\ &0\ &\frac{7}{4}\ &\frac{3}{4}\ &\frac{3}{4}\ &0\ &0\ &-\frac{39}{76}\ &\frac{47}{38}\ &\frac{9}{38}\ &\frac{9}{38}\ &-\frac{39}{76}\ &-\frac{39}{76}\ \\ &0\ &0\ &\frac{10}{7}\ &\frac{3}{7}\ &0\ &0\ &-\frac{39}{133}\ &-\frac{39}{133}\ &\frac{151}{133}\ &\frac{18}{133}\ &-\frac{39}{133}\ &-\frac{39}{133}\ \\ &0\ &0\ &0\ &\frac{13}{10}\ &0\ &0\ &-\frac{39}{190}\ &-\frac{39}{190}\ &-\frac{39}{190}\ &\frac{104}{95}\ &-\frac{39}{190}\ &-\frac{39}{190}\ \\ &0\ &0\ &0\ &0\ &\frac{16}{13}\ &0\ &-\frac{48}{247}\ &-\frac{48}{247}\ &-\frac{48}{247}\ &-\frac{48}{247}\ &\frac{256}{247}\ &-\frac{48}{247}\ \\ &0\ &0\ &0\ &0\ &0\ &\frac{19}{16}\ &-\frac{3}{16}\ &-\frac{3}{16}\ &-\frac{3}{16}\ &-\frac{3}{16}\ &-\frac{3}{16}\ &1\ \\\end{array} \right )\\\\->\ \ &\left (\begin{array} {ccccccc | cccccc} &4\ &3\ &3\ &0\ &0\ &0\ &\frac{46}{19}\ &\frac{27}{19}\ &\frac{27}{19}\ &-\frac{30}{19}\ &-\frac{30}{19}\ &-\frac{30}{19}\ \\ &0\ &\frac{7}{4}\ &\frac{3}{4}\ &0\ &0\ &0\ &-\frac{15}{38}\ &\frac{103}{76}\ &\frac{27}{76}\ &-\frac{15}{38}\ &-\frac{15}{38}\ &-\frac{15}{38}\ \\ &0\ &0\ &\frac{10}{7}\ &0\ &0\ &0\ &-\frac{30}{133}\ &-\frac{30}{133}\ &\frac{160}{133}\ &-\frac{30}{133}\ &-\frac{30}{133}\ &-\frac{30}{133}\ \\ &0\ &0\ &0\ &\frac{13}{10}\ &0\ &0\ &-\frac{39}{190}\ &-\frac{39}{190}\ &-\frac{39}{190}\ &\frac{104}{95}\ &-\frac{39}{190}\ &-\frac{39}{190}\ \\ &0\ &0\ &0\ &0\ &\frac{16}{13}\ &0\ &-\frac{48}{247}\ &-\frac{48}{247}\ &-\frac{48}{247}\ &-\frac{48}{247}\ &\frac{256}{247}\ &-\frac{48}{247}\ \\ &0\ &0\ &0\ &0\ &0\ &\frac{19}{16}\ &-\frac{3}{16}\ &-\frac{3}{16}\ &-\frac{3}{16}\ &-\frac{3}{16}\ &-\frac{3}{16}\ &1\ \\\end{array} \right )\\\\->\ \ &\left (\begin{array} {ccccccc | cccccc} &4\ &3\ &0\ &0\ &0\ &0\ &\frac{55}{19}\ &\frac{36}{19}\ &-\frac{21}{19}\ &-\frac{21}{19}\ &-\frac{21}{19}\ &-\frac{21}{19}\ \\ &0\ &\frac{7}{4}\ &0\ &0\ &0\ &0\ &-\frac{21}{76}\ &\frac{28}{19}\ &-\frac{21}{76}\ &-\frac{21}{76}\ &-\frac{21}{76}\ &-\frac{21}{76}\ \\ &0\ &0\ &\frac{10}{7}\ &0\ &0\ &0\ &-\frac{30}{133}\ &-\frac{30}{133}\ &\frac{160}{133}\ &-\frac{30}{133}\ &-\frac{30}{133}\ &-\frac{30}{133}\ \\ &0\ &0\ &0\ &\frac{13}{10}\ &0\ &0\ &-\frac{39}{190}\ &-\frac{39}{190}\ &-\frac{39}{190}\ &\frac{104}{95}\ &-\frac{39}{190}\ &-\frac{39}{190}\ \\ &0\ &0\ &0\ &0\ &\frac{16}{13}\ &0\ &-\frac{48}{247}\ &-\frac{48}{247}\ &-\frac{48}{247}\ &-\frac{48}{247}\ &\frac{256}{247}\ &-\frac{48}{247}\ \\ &0\ &0\ &0\ &0\ &0\ &\frac{19}{16}\ &-\frac{3}{16}\ &-\frac{3}{16}\ &-\frac{3}{16}\ &-\frac{3}{16}\ &-\frac{3}{16}\ &1\ \\\end{array} \right )\\\\->\ \ &\left (\begin{array} {ccccccc | cccccc} &4\ &0\ &0\ &0\ &0\ &0\ &\frac{64}{19}\ &-\frac{12}{19}\ &-\frac{12}{19}\ &-\frac{12}{19}\ &-\frac{12}{19}\ &-\frac{12}{19}\ \\ &0\ &\frac{7}{4}\ &0\ &0\ &0\ &0\ &-\frac{21}{76}\ &\frac{28}{19}\ &-\frac{21}{76}\ &-\frac{21}{76}\ &-\frac{21}{76}\ &-\frac{21}{76}\ \\ &0\ &0\ &\frac{10}{7}\ &0\ &0\ &0\ &-\frac{30}{133}\ &-\frac{30}{133}\ &\frac{160}{133}\ &-\frac{30}{133}\ &-\frac{30}{133}\ &-\frac{30}{133}\ \\ &0\ &0\ &0\ &\frac{13}{10}\ &0\ &0\ &-\frac{39}{190}\ &-\frac{39}{190}\ &-\frac{39}{190}\ &\frac{104}{95}\ &-\frac{39}{190}\ &-\frac{39}{190}\ \\ &0\ &0\ &0\ &0\ &\frac{16}{13}\ &0\ &-\frac{48}{247}\ &-\frac{48}{247}\ &-\frac{48}{247}\ &-\frac{48}{247}\ &\frac{256}{247}\ &-\frac{48}{247}\ \\ &0\ &0\ &0\ &0\ &0\ &\frac{19}{16}\ &-\frac{3}{16}\ &-\frac{3}{16}\ &-\frac{3}{16}\ &-\frac{3}{16}\ &-\frac{3}{16}\ &1\ \\\end{array} \right )\\\\&\color{grey}{将主对角线元素化为1}\\\\->\ \ &\left (\begin{array} {ccccccc | cccccc} &1\ &0\ &0\ &0\ &0\ &0\ &\frac{16}{19}\ &-\frac{3}{19}\ &-\frac{3}{19}\ &-\frac{3}{19}\ &-\frac{3}{19}\ &-\frac{3}{19}\ \\ &0\ &\frac{7}{4}\ &0\ &0\ &0\ &0\ &-\frac{21}{76}\ &\frac{28}{19}\ &-\frac{21}{76}\ &-\frac{21}{76}\ &-\frac{21}{76}\ &-\frac{21}{76}\ \\ &0\ &0\ &\frac{10}{7}\ &0\ &0\ &0\ &-\frac{30}{133}\ &-\frac{30}{133}\ &\frac{160}{133}\ &-\frac{30}{133}\ &-\frac{30}{133}\ &-\frac{30}{133}\ \\ &0\ &0\ &0\ &\frac{13}{10}\ &0\ &0\ &-\frac{39}{190}\ &-\frac{39}{190}\ &-\frac{39}{190}\ &\frac{104}{95}\ &-\frac{39}{190}\ &-\frac{39}{190}\ \\ &0\ &0\ &0\ &0\ &\frac{16}{13}\ &0\ &-\frac{48}{247}\ &-\frac{48}{247}\ &-\frac{48}{247}\ &-\frac{48}{247}\ &\frac{256}{247}\ &-\frac{48}{247}\ \\ &0\ &0\ &0\ &0\ &0\ &\frac{19}{16}\ &-\frac{3}{16}\ &-\frac{3}{16}\ &-\frac{3}{16}\ &-\frac{3}{16}\ &-\frac{3}{16}\ &1\ \\\end{array} \right )\\\\->\ \ &\left (\begin{array} {ccccccc | cccccc} &1\ &0\ &0\ &0\ &0\ &0\ &\frac{16}{19}\ &-\frac{3}{19}\ &-\frac{3}{19}\ &-\frac{3}{19}\ &-\frac{3}{19}\ &-\frac{3}{19}\ \\ &0\ &1\ &0\ &0\ &0\ &0\ &-\frac{3}{19}\ &\frac{16}{19}\ &-\frac{3}{19}\ &-\frac{3}{19}\ &-\frac{3}{19}\ &-\frac{3}{19}\ \\ &0\ &0\ &\frac{10}{7}\ &0\ &0\ &0\ &-\frac{30}{133}\ &-\frac{30}{133}\ &\frac{160}{133}\ &-\frac{30}{133}\ &-\frac{30}{133}\ &-\frac{30}{133}\ \\ &0\ &0\ &0\ &\frac{13}{10}\ &0\ &0\ &-\frac{39}{190}\ &-\frac{39}{190}\ &-\frac{39}{190}\ &\frac{104}{95}\ &-\frac{39}{190}\ &-\frac{39}{190}\ \\ &0\ &0\ &0\ &0\ &\frac{16}{13}\ &0\ &-\frac{48}{247}\ &-\frac{48}{247}\ &-\frac{48}{247}\ &-\frac{48}{247}\ &\frac{256}{247}\ &-\frac{48}{247}\ \\ &0\ &0\ &0\ &0\ &0\ &\frac{19}{16}\ &-\frac{3}{16}\ &-\frac{3}{16}\ &-\frac{3}{16}\ &-\frac{3}{16}\ &-\frac{3}{16}\ &1\ \\\end{array} \right )\\\\->\ \ &\left (\begin{array} {ccccccc | cccccc} &1\ &0\ &0\ &0\ &0\ &0\ &\frac{16}{19}\ &-\frac{3}{19}\ &-\frac{3}{19}\ &-\frac{3}{19}\ &-\frac{3}{19}\ &-\frac{3}{19}\ \\ &0\ &1\ &0\ &0\ &0\ &0\ &-\frac{3}{19}\ &\frac{16}{19}\ &-\frac{3}{19}\ &-\frac{3}{19}\ &-\frac{3}{19}\ &-\frac{3}{19}\ \\ &0\ &0\ &1\ &0\ &0\ &0\ &-\frac{3}{19}\ &-\frac{3}{19}\ &\frac{16}{19}\ &-\frac{3}{19}\ &-\frac{3}{19}\ &-\frac{3}{19}\ \\ &0\ &0\ &0\ &\frac{13}{10}\ &0\ &0\ &-\frac{39}{190}\ &-\frac{39}{190}\ &-\frac{39}{190}\ &\frac{104}{95}\ &-\frac{39}{190}\ &-\frac{39}{190}\ \\ &0\ &0\ &0\ &0\ &\frac{16}{13}\ &0\ &-\frac{48}{247}\ &-\frac{48}{247}\ &-\frac{48}{247}\ &-\frac{48}{247}\ &\frac{256}{247}\ &-\frac{48}{247}\ \\ &0\ &0\ &0\ &0\ &0\ &\frac{19}{16}\ &-\frac{3}{16}\ &-\frac{3}{16}\ &-\frac{3}{16}\ &-\frac{3}{16}\ &-\frac{3}{16}\ &1\ \\\end{array} \right )\\\\->\ \ &\left (\begin{array} {ccccccc | cccccc} &1\ &0\ &0\ &0\ &0\ &0\ &\frac{16}{19}\ &-\frac{3}{19}\ &-\frac{3}{19}\ &-\frac{3}{19}\ &-\frac{3}{19}\ &-\frac{3}{19}\ \\ &0\ &1\ &0\ &0\ &0\ &0\ &-\frac{3}{19}\ &\frac{16}{19}\ &-\frac{3}{19}\ &-\frac{3}{19}\ &-\frac{3}{19}\ &-\frac{3}{19}\ \\ &0\ &0\ &1\ &0\ &0\ &0\ &-\frac{3}{19}\ &-\frac{3}{19}\ &\frac{16}{19}\ &-\frac{3}{19}\ &-\frac{3}{19}\ &-\frac{3}{19}\ \\ &0\ &0\ &0\ &1\ &0\ &0\ &-\frac{3}{19}\ &-\frac{3}{19}\ &-\frac{3}{19}\ &\frac{16}{19}\ &-\frac{3}{19}\ &-\frac{3}{19}\ \\ &0\ &0\ &0\ &0\ &\frac{16}{13}\ &0\ &-\frac{48}{247}\ &-\frac{48}{247}\ &-\frac{48}{247}\ &-\frac{48}{247}\ &\frac{256}{247}\ &-\frac{48}{247}\ \\ &0\ &0\ &0\ &0\ &0\ &\frac{19}{16}\ &-\frac{3}{16}\ &-\frac{3}{16}\ &-\frac{3}{16}\ &-\frac{3}{16}\ &-\frac{3}{16}\ &1\ \\\end{array} \right )\\\\->\ \ &\left (\begin{array} {ccccccc | cccccc} &1\ &0\ &0\ &0\ &0\ &0\ &\frac{16}{19}\ &-\frac{3}{19}\ &-\frac{3}{19}\ &-\frac{3}{19}\ &-\frac{3}{19}\ &-\frac{3}{19}\ \\ &0\ &1\ &0\ &0\ &0\ &0\ &-\frac{3}{19}\ &\frac{16}{19}\ &-\frac{3}{19}\ &-\frac{3}{19}\ &-\frac{3}{19}\ &-\frac{3}{19}\ \\ &0\ &0\ &1\ &0\ &0\ &0\ &-\frac{3}{19}\ &-\frac{3}{19}\ &\frac{16}{19}\ &-\frac{3}{19}\ &-\frac{3}{19}\ &-\frac{3}{19}\ \\ &0\ &0\ &0\ &1\ &0\ &0\ &-\frac{3}{19}\ &-\frac{3}{19}\ &-\frac{3}{19}\ &\frac{16}{19}\ &-\frac{3}{19}\ &-\frac{3}{19}\ \\ &0\ &0\ &0\ &0\ &1\ &0\ &-\frac{3}{19}\ &-\frac{3}{19}\ &-\frac{3}{19}\ &-\frac{3}{19}\ &\frac{16}{19}\ &-\frac{3}{19}\ \\ &0\ &0\ &0\ &0\ &0\ &\frac{19}{16}\ &-\frac{3}{16}\ &-\frac{3}{16}\ &-\frac{3}{16}\ &-\frac{3}{16}\ &-\frac{3}{16}\ &1\ \\\end{array} \right )\\\\->\ \ &\left (\begin{array} {ccccccc | cccccc} &1\ &0\ &0\ &0\ &0\ &0\ &\frac{16}{19}\ &-\frac{3}{19}\ &-\frac{3}{19}\ &-\frac{3}{19}\ &-\frac{3}{19}\ &-\frac{3}{19}\ \\ &0\ &1\ &0\ &0\ &0\ &0\ &-\frac{3}{19}\ &\frac{16}{19}\ &-\frac{3}{19}\ &-\frac{3}{19}\ &-\frac{3}{19}\ &-\frac{3}{19}\ \\ &0\ &0\ &1\ &0\ &0\ &0\ &-\frac{3}{19}\ &-\frac{3}{19}\ &\frac{16}{19}\ &-\frac{3}{19}\ &-\frac{3}{19}\ &-\frac{3}{19}\ \\ &0\ &0\ &0\ &1\ &0\ &0\ &-\frac{3}{19}\ &-\frac{3}{19}\ &-\frac{3}{19}\ &\frac{16}{19}\ &-\frac{3}{19}\ &-\frac{3}{19}\ \\ &0\ &0\ &0\ &0\ &1\ &0\ &-\frac{3}{19}\ &-\frac{3}{19}\ &-\frac{3}{19}\ &-\frac{3}{19}\ &\frac{16}{19}\ &-\frac{3}{19}\ \\ &0\ &0\ &0\ &0\ &0\ &1\ &-\frac{3}{19}\ &-\frac{3}{19}\ &-\frac{3}{19}\ &-\frac{3}{19}\ &-\frac{3}{19}\ &\frac{16}{19}\ \\\end{array} \right )\\\\&\color{grey}{所求的逆矩阵为：}\\&\begin{pmatrix} &\frac{16}{19}\ &-\frac{3}{19}\ &-\frac{3}{19}\ &-\frac{3}{19}\ &-\frac{3}{19}\ &-\frac{3}{19}\ \\ &-\frac{3}{19}\ &\frac{16}{19}\ &-\frac{3}{19}\ &-\frac{3}{19}\ &-\frac{3}{19}\ &-\frac{3}{19}\ \\ &-\frac{3}{19}\ &-\frac{3}{19}\ &\frac{16}{19}\ &-\frac{3}{19}\ &-\frac{3}{19}\ &-\frac{3}{19}\ \\ &-\frac{3}{19}\ &-\frac{3}{19}\ &-\frac{3}{19}\ &\frac{16}{19}\ &-\frac{3}{19}\ &-\frac{3}{19}\ \\ &-\frac{3}{19}\ &-\frac{3}{19}\ &-\frac{3}{19}\ &-\frac{3}{19}\ &\frac{16}{19}\ &-\frac{3}{19}\ \\ &-\frac{3}{19}\ &-\frac{3}{19}\ &-\frac{3}{19}\ &-\frac{3}{19}\ &-\frac{3}{19}\ &\frac{16}{19}\ \end{pmatrix}\end{aligned}$$
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矩阵的初等变换：
定义：对矩阵的行（列）施行下列三种变换都成为矩阵的初等变换：
（1）互换矩阵两行（列）的位置；
（2）用非零常数λ乘矩阵的某行（列）；
（3）将矩阵某行（列）的γ倍加到矩阵的另一行（列）上。
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