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` ,