# nullspace

nullspace(M)

Basis for nullspace of `M`.

## Examples

In the Julia programming language, the function nullspace(M)

Compute a basis for the nullspace of matrix `M`.

``````julia> M = [1 2 3; 4 5 6; 7 8 9];
julia> nullspace(M)
3×1 Array{Float64,2}:
-0.40824829046386296
-0.8164965809277263
0.4082482904638631``````

Provide common examples of its use:

1. Find the nullspace of a matrix:

``````julia> A = [1 2 3; 4 5 6; 7 8 9];
julia> nullspace(A)
3×1 Array{Float64,2}:
-0.40824829046386296
-0.8164965809277263
0.4082482904638631``````

This example computes a basis for the nullspace of matrix `A`.

2. Solve a system of linear equations:
``````julia> B = [1 2 3 4; 5 6 7 8; 9 10 11 12];
julia> nullspace(B)
4×1 Array{Float64,2}:
-0.2366322821299352
0.4714045207910337
-0.7071067811865475
0.4714045207910339``````

In this example, the nullspace of matrix `B` is computed, which can be useful for solving systems of linear equations.

Common mistake example:

``````julia> C = [1 2 3; 4 5 6]
julia> nullspace(C)
ERROR: ArgumentError: expected a 2-dimensional array``````

In this example, the input matrix `C` is not a 2-dimensional array. The `nullspace` function expects a 2-dimensional matrix as its argument. Make sure to provide a valid matrix to the function to avoid this error.