Solving A*X=B : simult

### 2.52.4 Solving A*X=B : `simult`

`simult` is used to solve a linear system of equations (resp. several linear systems of equations with the same matrix `A`) written in matrix form (see also 2.31.17) :

`A*X=b (resp A*X=B)`

`simult` takes as arguments the matrix `A` of the system and the column vector (i.e. a one column matrix) `b` of the second member of the system (resp. the matrix `B` whose columns are the vectors `b` of the second members of the different systems).
The result is a column vector, solution of the system (resp. a matrix whose columns are the solutions of the different systems).
For example, to solve the system :

⎧ ⎨ ⎩ |
3x + y | = | −2
3x +2y | = | 2

input :

`simult([[3,1],[3,2]],[[-2],[2]])`

Output :

`[[-2],[4]]`

Hence x=−2 and y=4 is the solution.
Input :

`simult([[3,1],[3,2]],[[-2,1],[2,2]])`

Output :

`[[-2,0],[4,1]]`

Hence x=−2 and y=4 is the solution of

⎧ ⎨ ⎩ |
3x + y | = | −2
3x +2y | = | 2

whereas x=0 and y=1 is the solution of

⎧ ⎨ ⎩ |
3x + y | = | 1
3x +2y | = | 2