How to find the span of a matrix in matlab?

I am trying to find the span of a matrix but im not sure how to ask matlab to find it for me.

Let A = [−1 −5 −1 10 0 5; 1 5 0 −4 0 −5;2 10 −1 −2 −1 −7;−1 −5 2 −8 2 −1] . Find spanning sets for N (A) and col(A)

this is the question but im not sure how to ask it on matlab.

Answer 1

[Matt J]

You can use this,

https://www.mathworks.com/matlabcentral/fileexchange/77437-extract-linearly-independent-subset-of-matrix-columns

A = [-1 -5 -1 10 0 5; 1 5 0 -4 0 -5;2 10 -1 -2 -1 -7;-1 -5 2 -8 2 -1]

A = 4×6

-1 -5 -1 10 0 5 1 5 0 -4 0 -5 2 10 -1 -2 -1 -7 -1 -5 2 -8 2 -1

 Asub=licols(A)

Asub = 4×3

-5 10 5 5 -4 -5 10 -2 -7 -5 -8 -1

[Torsten]

And if by N(A) you mean the kernel of A, you can use:

A = [-1 -5 -1 10 0 5; 1 5 0 -4 0 -5;2 10 -1 -2 -1 -7;-1 -5 2 -8 2 -1]

A = 4×6

-1 -5 -1 10 0 5 1 5 0 -4 0 -5 2 10 -1 -2 -1 -7 -1 -5 2 -8 2 -1

null(A)

ans = 6×3

-0.8674 0.4588 0.0506 0.2671 0.1026 0.2325 -0.1868 -0.4006 0.8735 -0.0311 -0.0668 0.1456 0.3555 0.7434 0.3784 0.1185 0.2478 0.1261

Together with @Matt J 's answer, this shows that

https://math.libretexts.org/Bookshelves/Linear_Algebra/Book%3A_Linear_Algebra_(Schilling_Nachtergaele_and_Lankham)/06%3A_Linear_Maps/6.05%3A_The_dimension_formula

is true.

Answer 2

[Catalytic]

Use orth and null,

A = [-1 -5 -1 10 0 5; 1 5 0 -4 0 -5;2 10 -1 -2 -1 -7;-1 -5 2 -8 2 -1];

spanset=orth(A)

spanset = 4×3

0.6338 0.3530 0.6882 -0.4482 0.0376 0.3935 -0.6224 0.4626 0.3359 -0.0998 -0.8124 0.5086

rank([A,spanset])==rank(A)

ans = logical
   1