\begin{patch}{ExMatrixBasicFunctionPatch1}
\begin{paste}{ExMatrixBasicFunctionFull1}{ExMatrixBasicFunctionEmpty1}
\pastebutton{ExMatrixBasicFunctionFull1}{\hidepaste}
\tab{5}\spadcommand{m1 := matrix([[1,-2,1],[4,2,-4]])\bound{m1 }}
\indentrel{3}\begin{verbatim}
        Ú1  - 2   1 ¿
   (1)  ³           ³
        À4   2   - 4Ù
                                   Type: Matrix Integer
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ExMatrixBasicFunctionEmpty1}
\begin{paste}{ExMatrixBasicFunctionEmpty1}{ExMatrixBasicFunctionPatch1}
\pastebutton{ExMatrixBasicFunctionEmpty1}{\showpaste}
\tab{5}\spadcommand{m1 := matrix([[1,-2,1],[4,2,-4]])\bound{m1 }}
\end{paste}\end{patch}

\begin{patch}{ExMatrixBasicFunctionPatch2}
\begin{paste}{ExMatrixBasicFunctionFull2}{ExMatrixBasicFunctionEmpty2}
\pastebutton{ExMatrixBasicFunctionFull2}{\hidepaste}
\tab{5}\spadcommand{m2 := matrix([[1,0,2],[20,30,10],[0,200,100]])\bound{m2 }}
\indentrel{3}\begin{verbatim}
        Ú1    0    2 ¿
        ³            ³
   (2)  ³20  30   10 ³
        ³            ³
        À0   200  100Ù
                                   Type: Matrix Integer
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ExMatrixBasicFunctionEmpty2}
\begin{paste}{ExMatrixBasicFunctionEmpty2}{ExMatrixBasicFunctionPatch2}
\pastebutton{ExMatrixBasicFunctionEmpty2}{\showpaste}
\tab{5}\spadcommand{m2 := matrix([[1,0,2],[20,30,10],[0,200,100]])\bound{m2 }}
\end{paste}\end{patch}

\begin{patch}{ExMatrixBasicFunctionPatch3}
\begin{paste}{ExMatrixBasicFunctionFull3}{ExMatrixBasicFunctionEmpty3}
\pastebutton{ExMatrixBasicFunctionFull3}{\hidepaste}
\tab{5}\spadcommand{m3 := matrix([[1,2,3],[2,4,6]])\bound{m3 }}
\indentrel{3}\begin{verbatim}
        Ú1  2  3¿
   (3)  ³       ³
        À2  4  6Ù
                                   Type: Matrix Integer
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ExMatrixBasicFunctionEmpty3}
\begin{paste}{ExMatrixBasicFunctionEmpty3}{ExMatrixBasicFunctionPatch3}
\pastebutton{ExMatrixBasicFunctionEmpty3}{\showpaste}
\tab{5}\spadcommand{m3 := matrix([[1,2,3],[2,4,6]])\bound{m3 }}
\end{paste}\end{patch}

\begin{patch}{ExMatrixBasicFunctionPatch4}
\begin{paste}{ExMatrixBasicFunctionFull4}{ExMatrixBasicFunctionEmpty4}
\pastebutton{ExMatrixBasicFunctionFull4}{\hidepaste}
\tab{5}\spadcommand{m1 + m3\free{m1 }\free{m3 }}
\indentrel{3}\begin{verbatim}
        Ú2  0  4¿
   (4)  ³       ³
        À6  6  2Ù
                                   Type: Matrix Integer
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ExMatrixBasicFunctionEmpty4}
\begin{paste}{ExMatrixBasicFunctionEmpty4}{ExMatrixBasicFunctionPatch4}
\pastebutton{ExMatrixBasicFunctionEmpty4}{\showpaste}
\tab{5}\spadcommand{m1 + m3\free{m1 }\free{m3 }}
\end{paste}\end{patch}

\begin{patch}{ExMatrixBasicFunctionPatch5}
\begin{paste}{ExMatrixBasicFunctionFull5}{ExMatrixBasicFunctionEmpty5}
\pastebutton{ExMatrixBasicFunctionFull5}{\hidepaste}
\tab{5}\spadcommand{100 * m1\free{m1 }}
\indentrel{3}\begin{verbatim}
        Ú100  - 200   100 ¿
   (5)  ³                 ³
        À400   200   - 400Ù
                                   Type: Matrix Integer
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ExMatrixBasicFunctionEmpty5}
\begin{paste}{ExMatrixBasicFunctionEmpty5}{ExMatrixBasicFunctionPatch5}
\pastebutton{ExMatrixBasicFunctionEmpty5}{\showpaste}
\tab{5}\spadcommand{100 * m1\free{m1 }}
\end{paste}\end{patch}

\begin{patch}{ExMatrixBasicFunctionPatch6}
\begin{paste}{ExMatrixBasicFunctionFull6}{ExMatrixBasicFunctionEmpty6}
\pastebutton{ExMatrixBasicFunctionFull6}{\hidepaste}
\tab{5}\spadcommand{m1 * m2\free{m1 }\free{m2 }}
\indentrel{3}\begin{verbatim}
        Ú- 39   140    82  ¿
   (6)  ³                  ³
        À 44   - 740  - 372Ù
                                   Type: Matrix Integer
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ExMatrixBasicFunctionEmpty6}
\begin{paste}{ExMatrixBasicFunctionEmpty6}{ExMatrixBasicFunctionPatch6}
\pastebutton{ExMatrixBasicFunctionEmpty6}{\showpaste}
\tab{5}\spadcommand{m1 * m2\free{m1 }\free{m2 }}
\end{paste}\end{patch}

\begin{patch}{ExMatrixBasicFunctionPatch7}
\begin{paste}{ExMatrixBasicFunctionFull7}{ExMatrixBasicFunctionEmpty7}
\pastebutton{ExMatrixBasicFunctionFull7}{\hidepaste}
\tab{5}\spadcommand{-m1 + m3 * m2\free{m1 }\free{m2 }\free{m3 }}
\indentrel{3}\begin{verbatim}
        Ú40  662   321¿
   (7)  ³             ³
        À78  1318  648Ù
                                   Type: Matrix Integer
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ExMatrixBasicFunctionEmpty7}
\begin{paste}{ExMatrixBasicFunctionEmpty7}{ExMatrixBasicFunctionPatch7}
\pastebutton{ExMatrixBasicFunctionEmpty7}{\showpaste}
\tab{5}\spadcommand{-m1 + m3 * m2\free{m1 }\free{m2 }\free{m3 }}
\end{paste}\end{patch}

\begin{patch}{ExMatrixBasicFunctionPatch8}
\begin{paste}{ExMatrixBasicFunctionFull8}{ExMatrixBasicFunctionEmpty8}
\pastebutton{ExMatrixBasicFunctionFull8}{\hidepaste}
\tab{5}\spadcommand{m3 *vector([1,0,1])\free{m3 }}
\indentrel{3}\begin{verbatim}
   (8)  [4,8]
                                   Type: Vector Integer
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ExMatrixBasicFunctionEmpty8}
\begin{paste}{ExMatrixBasicFunctionEmpty8}{ExMatrixBasicFunctionPatch8}
\pastebutton{ExMatrixBasicFunctionEmpty8}{\showpaste}
\tab{5}\spadcommand{m3 *vector([1,0,1])\free{m3 }}
\end{paste}\end{patch}

\begin{patch}{ExRankMatrixPatch1}
\begin{paste}{ExRankMatrixFull1}{ExRankMatrixEmpty1}
\pastebutton{ExRankMatrixFull1}{\hidepaste}
\tab{5}\spadcommand{rank(matrix([[0,4,1],[5,3,-7],[-5,5,9]]))}
\indentrel{3}\begin{verbatim}
   (1)  2
                                  Type: PositiveInteger
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ExRankMatrixEmpty1}
\begin{paste}{ExRankMatrixEmpty1}{ExRankMatrixPatch1}
\pastebutton{ExRankMatrixEmpty1}{\showpaste}
\tab{5}\spadcommand{rank(matrix([[0,4,1],[5,3,-7],[-5,5,9]]))}
\end{paste}\end{patch}

\begin{patch}{ExTraceMatrixPatch1}
\begin{paste}{ExTraceMatrixFull1}{ExTraceMatrixEmpty1}
\pastebutton{ExTraceMatrixFull1}{\hidepaste}
\tab{5}\spadcommand{trace( matrix([[1,x,x**2,x**3],[1,y,y**2,y**3],[1,z,z**2,z**3],[1,u,u**2,u**3]]) )}
\indentrel{3}\begin{verbatim}
         2        3
   (1)  z  + y + u  + 1
                               Type: Polynomial Integer
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ExTraceMatrixEmpty1}
\begin{paste}{ExTraceMatrixEmpty1}{ExTraceMatrixPatch1}
\pastebutton{ExTraceMatrixEmpty1}{\showpaste}
\tab{5}\spadcommand{trace( matrix([[1,x,x**2,x**3],[1,y,y**2,y**3],[1,z,z**2,z**3],[1,u,u**2,u**3]]) )}
\end{paste}\end{patch}

\begin{patch}{ExInverseMatrixPatch1}
\begin{paste}{ExInverseMatrixFull1}{ExInverseMatrixEmpty1}
\pastebutton{ExInverseMatrixFull1}{\hidepaste}
\tab{5}\spadcommand{inverse(matrix([[1,2,1],[-2,3,4],[-1,5,6]]))}
\indentrel{3}\begin{verbatim}
        Ú  2        5 ¿
        ³- Ä  - 1   Ä ³
        ³  7        7 ³
        ³             ³
   (1)  ³ 8          6³
        ³ Ä    1   - ij
        ³ 7          7³
        ³             ³
        À- 1  - 1   1 Ù
               Type: Union(Matrix Fraction Integer,...)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ExInverseMatrixEmpty1}
\begin{paste}{ExInverseMatrixEmpty1}{ExInverseMatrixPatch1}
\pastebutton{ExInverseMatrixEmpty1}{\showpaste}
\tab{5}\spadcommand{inverse(matrix([[1,2,1],[-2,3,4],[-1,5,6]]))}
\end{paste}\end{patch}

\begin{patch}{ExConstructMatrixPatch1}
\begin{paste}{ExConstructMatrixFull1}{ExConstructMatrixEmpty1}
\pastebutton{ExConstructMatrixFull1}{\hidepaste}
\tab{5}\spadcommand{diagonalMatrix([1,2,3,2,1])}
\indentrel{3}\begin{verbatim}
        Ú1  0  0  0  0¿
        ³             ³
        ³0  2  0  0  0³
        ³             ³
   (1)  ³0  0  3  0  0³
        ³             ³
        ³0  0  0  2  0³
        ³             ³
        À0  0  0  0  1Ù
                                   Type: Matrix Integer
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ExConstructMatrixEmpty1}
\begin{paste}{ExConstructMatrixEmpty1}{ExConstructMatrixPatch1}
\pastebutton{ExConstructMatrixEmpty1}{\showpaste}
\tab{5}\spadcommand{diagonalMatrix([1,2,3,2,1])}
\end{paste}\end{patch}

\begin{patch}{ExConstructMatrixPatch2}
\begin{paste}{ExConstructMatrixFull2}{ExConstructMatrixEmpty2}
\pastebutton{ExConstructMatrixFull2}{\hidepaste}
\tab{5}\spadcommand{subMatrix(matrix([[0,1,2,3,4],[5,6,7,8,9],[10,11,12,13,14]]), 1,3,2,4)}
\indentrel{3}\begin{verbatim}
        Ú1   2   3 ¿
        ³          ³
   (2)  ³6   7   8 ³
        ³          ³
        À11  12  13Ù
                                   Type: Matrix Integer
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ExConstructMatrixEmpty2}
\begin{paste}{ExConstructMatrixEmpty2}{ExConstructMatrixPatch2}
\pastebutton{ExConstructMatrixEmpty2}{\showpaste}
\tab{5}\spadcommand{subMatrix(matrix([[0,1,2,3,4],[5,6,7,8,9],[10,11,12,13,14]]), 1,3,2,4)}
\end{paste}\end{patch}

\begin{patch}{ExConstructMatrixPatch3}
\begin{paste}{ExConstructMatrixFull3}{ExConstructMatrixEmpty3}
\pastebutton{ExConstructMatrixFull3}{\hidepaste}
\tab{5}\spadcommand{horizConcat(matrix([[1,2,3],[6,7,8]]),matrix([[11,12,13],[55,77,88]]))}
\indentrel{3}\begin{verbatim}
        Ú1  2  3  11  12  13¿
   (3)  ³                   ³
        À6  7  8  55  77  88Ù
                                   Type: Matrix Integer
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ExConstructMatrixEmpty3}
\begin{paste}{ExConstructMatrixEmpty3}{ExConstructMatrixPatch3}
\pastebutton{ExConstructMatrixEmpty3}{\showpaste}
\tab{5}\spadcommand{horizConcat(matrix([[1,2,3],[6,7,8]]),matrix([[11,12,13],[55,77,88]]))}
\end{paste}\end{patch}

\begin{patch}{ExConstructMatrixPatch4}
\begin{paste}{ExConstructMatrixFull4}{ExConstructMatrixEmpty4}
\pastebutton{ExConstructMatrixFull4}{\hidepaste}
\tab{5}\spadcommand{vertConcat(matrix([[1,2,3],[6,7,8]]),matrix([[11,12,13],[55,77,88]]))}
\indentrel{3}\begin{verbatim}
        Ú1   2   3 ¿
        ³          ³
        ³6   7   8 ³
   (4)  ³          ³
        ³11  12  13³
        ³          ³
        À55  77  88Ù
                                   Type: Matrix Integer
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ExConstructMatrixEmpty4}
\begin{paste}{ExConstructMatrixEmpty4}{ExConstructMatrixPatch4}
\pastebutton{ExConstructMatrixEmpty4}{\showpaste}
\tab{5}\spadcommand{vertConcat(matrix([[1,2,3],[6,7,8]]),matrix([[11,12,13],[55,77,88]]))}
\end{paste}\end{patch}

\begin{patch}{ExConstructMatrixPatch5}
\begin{paste}{ExConstructMatrixFull5}{ExConstructMatrixEmpty5}
\pastebutton{ExConstructMatrixFull5}{\hidepaste}
\tab{5}\spadcommand{b:=matrix([[0,1,2,3,4],[5,6,7,8,9],[10,11,12,13,14]])\bound{b }}
\indentrel{3}\begin{verbatim}
        Ú0   1   2   3   4 ¿
        ³                  ³
   (5)  ³5   6   7   8   9 ³
        ³                  ³
        À10  11  12  13  14Ù
                                   Type: Matrix Integer
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ExConstructMatrixEmpty5}
\begin{paste}{ExConstructMatrixEmpty5}{ExConstructMatrixPatch5}
\pastebutton{ExConstructMatrixEmpty5}{\showpaste}
\tab{5}\spadcommand{b:=matrix([[0,1,2,3,4],[5,6,7,8,9],[10,11,12,13,14]])\bound{b }}
\end{paste}\end{patch}

\begin{patch}{ExConstructMatrixPatch6}
\begin{paste}{ExConstructMatrixFull6}{ExConstructMatrixEmpty6}
\pastebutton{ExConstructMatrixFull6}{\hidepaste}
\tab{5}\spadcommand{setsubMatrix!(b,1,1,transpose(subMatrix(b,1,3,1,3)))\free{b }}
\indentrel{3}\begin{verbatim}
        Ú0  5  10  3   4 ¿
        ³                ³
   (6)  ³1  6  11  8   9 ³
        ³                ³
        À2  7  12  13  14Ù
                                   Type: Matrix Integer
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ExConstructMatrixEmpty6}
\begin{paste}{ExConstructMatrixEmpty6}{ExConstructMatrixPatch6}
\pastebutton{ExConstructMatrixEmpty6}{\showpaste}
\tab{5}\spadcommand{setsubMatrix!(b,1,1,transpose(subMatrix(b,1,3,1,3)))\free{b }}
\end{paste}\end{patch}

\begin{patch}{ExDeterminantMatrixPatch1}
\begin{paste}{ExDeterminantMatrixFull1}{ExDeterminantMatrixEmpty1}
\pastebutton{ExDeterminantMatrixFull1}{\hidepaste}
\tab{5}\spadcommand{determinant(matrix([[1,2,3,4],[2,3,2,5],[3,4,5,6],[4,1,6,7]]))}
\indentrel{3}\begin{verbatim}
   (1)  - 48
                                          Type: Integer
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ExDeterminantMatrixEmpty1}
\begin{paste}{ExDeterminantMatrixEmpty1}{ExDeterminantMatrixPatch1}
\pastebutton{ExDeterminantMatrixEmpty1}{\showpaste}
\tab{5}\spadcommand{determinant(matrix([[1,2,3,4],[2,3,2,5],[3,4,5,6],[4,1,6,7]]))}
\end{paste}\end{patch}