linsolve

Scilab Function
Last update : April 1993

linsolve - linear equation solver

### Calling Sequence

  `[x0,kerA]=linsolve(A,b [,x0])`

### Parameters

- `A`: a `na x ma` real matrix (possibly sparse)
- `b`: a `na x 1` vector (same row dimension as `A`)
- `x0`: a real vector
- `kerA`: a `ma x k` real matrix

### Description

`linsolve` computes all the solutions to `A*x+b=0`.

`x0` is a particular solution (if any) and `kerA=` nullspace of `A`. Any `x=x0+kerA*w` with arbitrary `w` satisfies `A*x+b=0`.

If compatible `x0` is given on entry, `x0` is returned. If not a compatible `x0`, if any, is returned.

### Examples

    A=rand(5,3)*rand(3,8);
    b=A*ones(8,1);[x,kerA]=linsolve(A,b);A*x+b   //compatible b
    b=ones(5,1);[x,kerA]=linsolve(A,b);A*x+b   //uncompatible b
    A=rand(5,5);[x,kerA]=linsolve(A,b), -inv(A)*b  //x is unique

### See Also

`inv`, `pinv`, `colcomp`, `im_inv`,