Scilab 6.0.1
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Scilab Help >> Linear Algebra > Linear Equations > linsolve

# linsolve

linear equation solver

### Syntax

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

### Arguments

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

// Benchmark with other linear sparse solver:

b = zeros(size(A,1),1);

tic();
res = umfpack(A,'\',b);
mprintf('\ntime needed to solve the system with umfpack: %.3f\n',toc());

tic();
res = linsolve(A,b);
mprintf('\ntime needed to solve the system with linsolve: %.3f\n',toc());

tic();
res = A\b;
mprintf('\ntime needed to solve the system with the backslash operator: %.3f\n',toc());```