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Q&A Matrix solution software

You could use Maxima. Some packages offer a GUI (Xmaxima or Wxmaxima, if I'm not mistaken), but you can use it in the terminal. Below, an interactive terminal Maxima session in which I define and ...

posted 2y ago by Quasímodo‭

Answer
#1: Initial revision by user avatar Quasímodo‭ · 2021-10-06T16:52:52Z (over 2 years ago)
You could use [Maxima][1]. Some packages offer a GUI (Xmaxima or Wxmaxima, if I'm not mistaken), but you can use it in the terminal.

Below, an interactive terminal Maxima session in which I define and invert the two-dimensional rotation matrix.

```
(%i3) m: matrix([cos(x), -sin(x)], [sin(x), cos(x)]);
                             [ cos(x)  - sin(x) ]
(%o3)                        [                  ]
                             [ sin(x)   cos(x)  ]
(%i4) m^^-1;
                  [       cos(x)              sin(x)       ]
                  [  -----------------   ----------------- ]
                  [     2         2         2         2    ]
                  [  sin (x) + cos (x)   sin (x) + cos (x) ]
(%o4)             [                                        ]
                  [        sin(x)             cos(x)       ]
                  [ - -----------------  ----------------- ]
                  [      2         2        2         2    ]
                  [   sin (x) + cos (x)  sin (x) + cos (x) ]
(%i5) trigsimp(%);
                             [  cos(x)   sin(x) ]
(%o5)                        [                  ]
                             [ - sin(x)  cos(x) ]
```

Note that Maxima is somewhat lazy and leaves even the most elementary trigonometric identities such as sin²(x)+cos²(x) unresolved. I used `trigsimp` on the last output expression, `%`, to simplify the output.

In Maxima, you can use the question mark to find help on a function or operator. For example, `? matrix`.

[1]: https://en.wikipedia.org/wiki/Maxima