ex2</titel></head> <body> <br><br>> with(linalg);</b><br> Take a matrix <br><br>> A:=matrix([[1,2],[3,4]]);</b><br> <center> <table> <tr> <td rowspan=2 align=middle><i>A</i> :=</td> <td>[ 1</td> <td align=right>2 ]</td> </tr> <tr> <td>[ 3</td> <td align=right>4 ]</td> </tr> </table> </center> And the identity matrix <br><br>> Id:=matrix([[1,0],[0,1]]);</b><br> <center> <table> <tr> <td rowspan=2 align=middle><i>Id</i> :=</td> <td>[ 1</td> <td align=right>0 ]</td> </tr> <tr> <td>[ 0</td> <td align=right>1 ]</td> </tr> </table> </center> Augment them <br><br>> B:=augment(A,Id);</b><br> <center> <table> <tr> <td rowspan=2 align=middle><i>B</i> :=</td> <td>[ 1</td> <td>2</td> <td>1</td> <td align=right>0 ]</td> </tr> <tr> <td>[ 3</td> <td>4</td> <td>0</td> <td align=right>1 ]</td> </tr> </table> </center> Look what happens when we do a row operation to this matrix: this operation is applied simultaneously to both <i>A</i> and <i>Id</i> <br><br>> C:=addrow(B,1,2,-3);</b><br> <center> <table> <tr> <td rowspan=2 align=middle><i>C</i> :=</td> <td>[ 1</td> <td>2</td> <td>1</td> <td align=right>0 ]</td> </tr> <tr> <td>[ 0</td> <td>-2</td> <td>-3</td> <td align=right>1 ]</td> </tr> </table> </center> Now do the Gauss-Jordan procedure <br><br>> F:=gaussjord(C);</b><br> <center> <table> <tr> <td rowspan=2 align=middle><i>F</i> :=</td> <td>[ 1</td> <td>0</td> <td>-2</td> <td align=right>1 ]</td> </tr> <tr> <td>[ 0</td> <td>1</td> <td>3/2</td> <td align=right>-1/2 ]</td> </tr> </table> </center> The left half of this matrix is the identity matrix, so the right part must be the inverse of <i>A</i>. <br><br>> FF:=matrix([[-2,1],[3/2,-1/2]]);</b><br> <center> <table> <tr> <td rowspan=2 align=middle><i>FF</i> :=</td> <td>[ -2</td> <td align=right>1 ]</td> </tr> <tr> <td>[ 3/2</td> <td align=right>-1/2 ]</td> </tr> </table> </center> Check it: <br><b>> evalm(A&*FF);</b><br> <center> <table> <tr> <td>[ 1</td> <td align=right>0 ]</td> </tr> <tr> <td>[ 0</td> <td align=right>1 ]</td> </tr> </table> </center> </body> </html>