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  1. 3周前
    2019-01-23 13:59:22

    -image-
    All Sky Lunar Eclipse Trail
    Credit: Chris Hetlage
    Location: Greensboro, Georgia, USA

  2. 2019-01-23 13:58:43

    -image-
    Eclipse Sequence and Reflection from French Lake
    Credit: Philippe Jacquot

  3. 2019-01-23 13:58:27

    -image-
    Lunar Eclipse Path above Papradno, Slovakia
    Credit: Ondrej Kralik

  4. 2019-01-23 13:58:05

    -image-
    Lunar Eclipse Path over Cologne Cathedral
    Credit: Dong Han
    Location: Cologne, Germany

  5. 2019-01-23 13:57:42

    -image-
    Lunar Eclipse Sequence over Sirene Observatory
    Credit: Cyprien Pouzenc
    Location: Lagarde d'Apt, Vaucluse, France

  6. 2019-01-23 13:56:36

    -image-
    Lunar Eclipse Sequence over Cologne Cathedral
    Credit: Martin Junius
    Location: Germany
    Details: https://photo.m-j-s.net/blog/2019/01/lunar-eclipse-21-jan-2019/

  7. 2019-01-23 13:53:23

    -image-
    Lunar Eclipse Rising over India
    Credit: Nikunj Rawal
    Location: Jamnagar, Gujarat India

  8. 2019-01-23 13:52:33

    -image-
    Lunar Eclipse Sequence over Rocket Garden
    Credit: Michael Seeley
    Location: Kennedy Space Center, Florida, USA

  9. 2019-01-23 13:51:29
    baishuxu 发表了帖子 这次月蚀的一些好看的照片

    图源:Total Lunar Eclipse: 2019 January


    -image-
    Lunar Eclipse Sequnce over 13th Century Church
    Credit: Rafael Schmall
    Location: Pusztatorony, Somogyvámos, Hungary

  10. 2019-01-23 12:55:42
    baishuxu 更新于 行列式解线性方程组

    @德洛奈曲面 这不就是李炯生的《线性代数》P71页 第二章第4节的习题1嘛……
    \[
    \color{purple}{
    \left\{
    \begin{split}
    x_1&+&&x_2&+&2&x_3&+&3&x_4&=&&1\\
    3x_1&-&&x_2&-&&x_3&-&2&x_4&=&-&4\\
    2x_1&+&3&x_2&-&&x_3&-&&x_4&=&-&6\\
    x_1&+&2&x_2&+&3&x_3&-&&x_4&=&-&4
    \end{split}
    \right. }
    \]
    \[
    D_a=\left|\begin{array}{ccccccc}
    1&1&2&3\\
    3&-1&-1&-2\\
    2&3&-1&-1\\
    1&2&3&-1
    \end{array}
    \right|
    \overset{r_2-3r_1\\r_3-2r_1\\r_4-r_1}{\overline{\overline{\hspace{3cm}}}}
    \left|\begin{array}{ccccccc}
    1&1&2&3\\
    0&-4&-7&-11\\
    0&1&-5&-7\\
    0&1&1&-4
    \end{array}
    \right|\\
    \overset{r_2\longleftrightarrow r_4}{\overline{\overline{\hspace{3cm}}}}
    {\color{red}-}\left|\begin{array}{ccccccc}
    1&1&2&3\\
    0&1&1&-4\\
    0&1&-5&-7\\
    0&-4&-7&-11
    \end{array}
    \right|
    \overset{r_3-r_2\\r_4+4r_2}{\overline{\overline{\hspace{3cm}}}}
    {\color{red}-}\left|\begin{array}{ccccccc}
    1&1&2&3\\
    0&1&1&-4\\
    0&0&-6&-3\\
    0&0&-3&-27
    \end{array}
    \right|\\
    \overset{r_3\longleftrightarrow r_4}{\overline{\overline{\hspace{3cm}}}}
    {\color{red}+}\left|\begin{array}{ccccccc}
    1&1&2&3\\
    0&1&1&-4\\
    0&0&-3&-27\\
    0&0&-6&-3\\
    \end{array}
    \right|
    \overset{r_4-2r_3}{\overline{\overline{\hspace{3cm}}}}
    {\color{red}+}\left|\begin{array}{ccccccc}
    1&1&2&3\\
    0&1&1&-4\\
    0&0&-3&-27\\
    0&0&0&51\\
    \end{array}
    \right|={\color{blue}-153}
    \]
    \[
    {D_a}_1=\left|\begin{array}{ccccccc}
    1&1&2&3\\
    -4&-1&-1&-2\\
    -6&3&-1&-1\\
    -4&2&3&-1
    \end{array}
    \right|
    \overset{r_2+4r_1\\r_3+6r_1\\r_4+4r_1}{\overline{\overline{\hspace{3cm}}}}
    \left|\begin{array}{ccccccc}
    1&1&2&3\\
    0&3&7&10\\
    0&9&11&17\\
    0&6&11&11
    \end{array}
    \right|\\
    \overset{\\r_3-3r_2\\r_4-2r_2}{\overline{\overline{\hspace{3cm}}}}
    \left|\begin{array}{ccccccc}
    1&1&2&3\\
    0&3&7&10\\
    0&0&-10&-13\\
    0&0&-3&-9
    \end{array}
    \right|=
    -3\left|\begin{array}{ccccccc}
    1&1&2&3\\
    0&3&7&10\\
    0&0&-10&-13\\
    0&0&1&3
    \end{array}
    \right|\\
    \overset{r_3\longleftrightarrow r_4}{\overline{\overline{\hspace{3cm}}}}
    \,{\color{red}+}3\left|\begin{array}{ccccccc}
    1&1&2&3\\
    0&3&7&10\\
    0&0&1&3\\
    0&0&-10&-13
    \end{array}
    \right|
    \overset{r_4+10r_3}{\overline{\overline{\hspace{3cm}}}}
    \,3\left|\begin{array}{ccccccc}
    1&1&2&3\\
    0&3&7&10\\
    0&0&1&3\\
    0&0&0&17
    \end{array}
    \right|
    ={\color{blue}153}
    \]
    \[
    {D_a}_2=\left|\begin{array}{ccccccc}
    1&1&2&3\\
    3&-4&-1&-2\\
    2&-6&-1&-1\\
    1&-4&3&-1
    \end{array}
    \right|
    \overset{r_2-3r_1\\r_3-2r_1\\r_4-r_1}{\overline{\overline{\hspace{3cm}}}}
    \left|\begin{array}{ccccccc}
    1&1&2&3\\
    0&-7&-7&-11\\
    0&-8&-5&-7\\
    0&-5&1&-4
    \end{array}
    \right|\\
    =
    -7\left|\begin{array}{ccccccc}
    1&1&2&3\\
    0&1&1&\frac{11}{7}\\
    0&-8&-5&-7\\
    0&-5&1&-4
    \end{array}
    \right|
    \overset{r_4+5r_2}{\overline{\overline{\hspace{3cm}}}}
    -7\left|\begin{array}{ccccccc}
    1&1&2&3\\
    0&1&1&\frac{11}{7}\\
    0&-8&-5&-7\\
    0&0&6&\frac{27}{7}
    \end{array}
    \right|\\
    \overset{r_3+8r_2}{\overline{\overline{\hspace{3cm}}}}
    -7\left|\begin{array}{ccccccc}
    1&1&2&3\\
    0&1&1&\frac{11}{7}\\
    0&0&3&\frac{39}{7}\\
    0&0&6&\frac{27}{7}
    \end{array}
    \right|
    \overset{r_4-2r_3}{\overline{\overline{\hspace{3cm}}}}
    -7\left|\begin{array}{ccccccc}
    1&1&2&3\\
    0&1&1&\frac{11}{7}\\
    0&0&3&\frac{39}{7}\\
    0&0&0&-\frac{51}{7}
    \end{array}
    \right|
    ={\color{blue}153}
    \]
    \[
    {D_a}_3=\left|\begin{array}{ccccccc}
    1&1&1&3\\
    3&-1&-4&-2\\
    2&3&-6&-1\\
    1&2&-4&-1
    \end{array}
    \right|
    \overset{r_2-3r_1\\r_3-2r_1\\r_4-r_1}{\overline{\overline{\hspace{3cm}}}}
    \left|\begin{array}{ccccccc}
    1&1&1&3\\
    0&-4&-7&-11\\
    0&1&-8&-7\\
    0&1&-5&-4
    \end{array}
    \right|\\
    \overset{r_2\longleftrightarrow r_3}{\overline{\overline{\hspace{3cm}}}}
    {\color{red}-}
    \left|\begin{array}{ccccccc}
    1&1&1&3\\
    0&1&-8&-7\\
    0&-4&-7&-11\\
    0&1&-5&-4
    \end{array}
    \right|
    \overset{r_3+4r_2\\r_4-r_2}{\overline{\overline{\hspace{3cm}}}}
    {\color{red}-}
    \left|\begin{array}{ccccccc}
    1&1&1&3\\
    0&1&-8&-7\\
    0&0&-39&-39\\
    0&0&3&3
    \end{array}
    \right|
    ={\color{blue}0}
    \]
    \[
    {D_a}_4=\left|\begin{array}{ccccccc}
    1&1&2&1\\
    3&-1&-1&-4\\
    2&3&-1&-6\\
    1&2&3&-4
    \end{array}
    \right|
    \overset{r_2-3r_1\\r_3-2r_1\\r_4-r_1}{\overline{\overline{\hspace{3cm}}}}
    \left|\begin{array}{ccccccc}
    1&1&2&1\\
    0&-4&-7&-7\\
    0&1&-5&-8\\
    0&1&1&-5
    \end{array}
    \right|\\
    \overset{r_2\longleftrightarrow r_4}{\overline{\overline{\hspace{3cm}}}}
    {\color{red}-}
    \left|\begin{array}{ccccccc}
    1&1&2&1\\
    0&1&1&-5\\
    0&1&-5&-8\\
    0&-4&-7&-7
    \end{array}
    \right|
    \overset{r_3+4r_2\\r_4+3r_2}{\overline{\overline{\hspace{3cm}}}}
    {\color{red}-}
    \left|\begin{array}{ccccccc}
    1&1&2&1\\
    0&1&1&-5\\
    0&0&-6&-3\\
    0&0&-3&-27
    \end{array}
    \right|\\
    \overset{r_3\longleftrightarrow r_4}{\overline{\overline{\hspace{3cm}}}}
    {\color{red}+}
    \left|\begin{array}{ccccccc}
    1&1&2&1\\
    0&1&1&-5\\
    0&0&-3&-27\\
    0&0&-6&-3
    \end{array}
    \right|
    \overset{r_4-2r_3}{\overline{\overline{\hspace{3cm}}}}
    \left|\begin{array}{ccccccc}
    1&1&2&1\\
    0&1&1&-5\\
    0&0&-3&-27\\
    0&0&0&51
    \end{array}
    \right|
    ={\color{blue}-153}
    \]
    \[
    \color{purple}{
    \left\{
    \begin{split}
    x_1&\,&&&&&&&&&=&-&1\\
    &&&x_2&&&&&&&=&-&1\\
    &&&&&&x_3&&&&=&&0\\
    &\,&&&&&&&&x_4&=&&1
    \end{split}
    \right. }
    \]
    \(\overline{\hspace{15cm}}\)
    \[
    \color{green}{
    \left\{
    \begin{split}
    2x_1&-&&x_2&+&3&x_3&+&2&x_4&=4\\
    3x_1&+&3&x_2&+&3&x_3&+&2&x_4&=6\\
    3x_1&-&2&x_2&-&&x_3&+&2&x_4&=6\\
    3x_1&-&&x_2&+&3&x_3&-&&x_4&=6
    \end{split}
    \right. }
    \]
    \[
    D_b=\left|\begin{array}{ccccccc}
    2&-1&3&2\\
    3&3&3&2\\
    3&-2&-1&2\\
    3&-1&3&-1
    \end{array}
    \right|=
    \,3\left|\begin{array}{ccccccc}
    2&-1&3&2\\
    1&1&1&\frac{2}{3}\\
    3&-2&-1&2\\
    3&-1&3&-1
    \end{array}
    \right|\\
    \overset{r_1\longleftrightarrow r_2}{\overline{\overline{\hspace{3cm}}}}
    {\color{red}-}3\left|\begin{array}{ccccccc}
    1&1&1&\frac{2}{3}\\
    2&-1&3&2\\
    3&-2&-1&2\\
    3&-1&3&-1
    \end{array}
    \right|
    \overset{r_2-2r_1\\r_3-3r_1\\r_4-3r_1}{\overline{\overline{\hspace{3cm}}}}
    {\color{red}-}3\left|\begin{array}{ccccccc}
    1&1&1&\frac{2}{3}\\
    0&-3&1&\frac{2}{3}\\
    0&-5&-4&0\\
    0&-4&0&-3
    \end{array}
    \right|\\
    ={\color{red}+}3\cdot4\left|\begin{array}{ccccccc}
    1&1&1&\frac{2}{3}\\
    0&-3&1&\frac{2}{3}\\
    0&-5&-4&0\\
    0&1&0&\frac{3}{4}
    \end{array}
    \right|
    \overset{r_2\longleftrightarrow r_4}{\overline{\overline{\hspace{3cm}}}}
    {\color{red}-}12\left|\begin{array}{ccccccc}
    1&1&1&\frac{2}{3}\\
    0&1&0&\frac{3}{4}\\
    0&-5&-4&0\\
    0&-3&1&\frac{2}{3}
    \end{array}
    \right|\\
    \overset{r_3+5r_2\\r_4+3r_2}{\overline{\overline{\hspace{3cm}}}}
    {\color{red}-}12\left|\begin{array}{ccccccc}
    1&1&1&\frac{2}{3}\\
    0&1&0&\frac{3}{4}\\
    0&0&-4&\frac{15}{4}\\
    0&0&1&\frac{35}{12}
    \end{array}
    \right|
    \overset{r_3\longleftrightarrow r_4}{\overline{\overline{\hspace{3cm}}}}
    {\color{red}+}12\left|\begin{array}{ccccccc}
    1&1&1&\frac{2}{3}\\
    0&1&0&\frac{3}{4}\\
    0&0&1&\frac{35}{12}\\
    0&0&-4&\frac{15}{4}
    \end{array}
    \right|\\
    \overset{r_4+4r_3}{\overline{\overline{\hspace{3cm}}}}
    {\color{red}+}12\left|\begin{array}{ccccccc}
    1&1&1&\frac{2}{3}\\
    0&1&0&\frac{3}{4}\\
    0&0&1&\frac{35}{12}\\
    0&0&0&\frac{185}{12}
    \end{array}
    \right|={\color{blue}185}
    \]
    \[
    {D_b}_1=\left|\begin{array}{ccccccc}
    4&-1&3&2\\
    6&3&3&2\\
    6&-2&-1&2\\
    6&-1&3&-1
    \end{array}
    \right|=
    \,4\left|\begin{array}{ccccccc}
    1&-\frac{1}{4}&\frac{3}{4}&\frac{1}{2}\\
    6&3&3&2\\
    6&-2&-1&2\\
    6&-1&3&-1
    \end{array}
    \right|\\
    \overset{r_2-6r_1\\r_3-6r_1\\r_4-6r_1}{\overline{\overline{\hspace{3cm}}}}
    \,4\left|\begin{array}{ccccccc}
    1&-\frac{1}{4}&\frac{3}{4}&\frac{1}{2}\\
    0&\frac{9}{2}&-\frac{3}{2}&-1\\
    0&-\frac{1}{2}&-\frac{11}{2}&-1\\
    0&\frac{1}{2}&-\frac{3}{2}&-4
    \end{array}
    \right|
    \overset{r_2\longleftrightarrow r_4}{\overline{\overline{\hspace{3cm}}}}
    {\color{red}-}4\left|\begin{array}{ccccccc}
    1&-\frac{1}{4}&\frac{3}{4}&\frac{1}{2}\\
    0&\frac{1}{2}&-\frac{3}{2}&-4\\
    0&-\frac{1}{2}&-\frac{11}{2}&-1\\
    0&\frac{9}{2}&-\frac{3}{2}&-1
    \end{array}
    \right|\\
    \overset{r_3+r_2\\r_4-9r_2}{\overline{\overline{\hspace{3cm}}}}
    {\color{red}-}4\left|\begin{array}{ccccccc}
    1&-\frac{1}{4}&\frac{3}{4}&\frac{1}{2}\\
    0&\frac{1}{2}&-\frac{3}{2}&-4\\
    0&0&-7&-5\\
    0&0&12&35
    \end{array}
    \right|
    \overset{r_4+r_3}{\overline{\overline{\hspace{3cm}}}}
    {\color{red}-}4\left|\begin{array}{ccccccc}
    1&-\frac{1}{4}&\frac{3}{4}&\frac{1}{2}\\
    0&\frac{1}{2}&-\frac{3}{2}&-4\\
    0&0&-7&-5\\
    0&0&5&30
    \end{array}
    \right|\\
    \overset{r_3+5r_2\\r_4+3r_2}{\overline{\overline{\hspace{3cm}}}}
    {\color{red}-}4\cdot5\left|\begin{array}{ccccccc}
    1&-\frac{1}{4}&\frac{3}{4}&\frac{1}{2}\\
    0&\frac{1}{2}&-\frac{3}{2}&-4\\
    0&0&-7&-5\\
    0&0&1&6
    \end{array}
    \right|
    \overset{r_3\longleftrightarrow r_4}{\overline{\overline{\hspace{3cm}}}}
    {\color{red}+}20\left|\begin{array}{ccccccc}
    1&-\frac{1}{4}&\frac{3}{4}&\frac{1}{2}\\
    0&\frac{1}{2}&-\frac{3}{2}&-4\\
    0&0&1&6\\
    0&0&-7&-5
    \end{array}
    \right|\\
    \overset{r_4+7r_3}{\overline{\overline{\hspace{3cm}}}}
    \,20\left|\begin{array}{ccccccc}
    1&-\frac{1}{4}&\frac{3}{4}&\frac{1}{2}\\
    0&\frac{1}{2}&-\frac{3}{2}&-4\\
    0&0&1&6\\
    0&0&0&37
    \end{array}
    \right|={\color{blue}370}
    \]
    \[
    {D_b}_2=\left|\begin{array}{ccccccc}
    2&4&3&2\\
    3&6&3&2\\
    3&6&-1&2\\
    3&6&3&-1
    \end{array}
    \right|
    \overset{l_2-2r_1}{\overline{\overline{\hspace{3cm}}}}
    \left|\begin{array}{ccccccc}
    2&0&3&2\\
    3&0&3&2\\
    3&0&-1&2\\
    3&0&3&-1
    \end{array}
    \right|
    =\color{blue}{0}
    \]
    \[
    {D_b}_3=\left|\begin{array}{ccccccc}
    2&-1&4&2\\
    3&3&6&2\\
    3&-2&6&2\\
    3&-1&6&-1
    \end{array}
    \right|
    \overset{l_3-2r_1}{\overline{\overline{\hspace{3cm}}}}
    \left|\begin{array}{ccccccc}
    2&-1&0&2\\
    3&3&0&2\\
    3&-2&0&2\\
    3&-1&0&-1
    \end{array}
    \right|
    =\color{blue}{0}
    \]
    \[
    {D_b}_4=\left|\begin{array}{ccccccc}
    2&-1&3&4\\
    3&3&3&6\\
    3&-2&-1&6\\
    3&-1&3&6
    \end{array}
    \right|
    \overset{l_4-2r_1}{\overline{\overline{\hspace{3cm}}}}
    \left|\begin{array}{ccccccc}
    2&-1&3&0\\
    3&3&3&0\\
    3&-2&-1&0\\
    3&-1&3&0
    \end{array}
    \right|
    =\color{blue}{0}
    \]
    \[
    \color{green}{
    \left\{
    \begin{split}
    x_1&\,&&&&&&&&&=&2\\
    &&&x_2&&&&&&&=&0\\
    &&&&&&x_3&&&&=&0\\
    &\,&&&&&&&&x_4&=&0
    \end{split}
    \right. }
    \]

    就服你 /< /good

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