Permutation Matrix on Matlab

Hi I am new on MATLAB. In my project I am using matlab. Some step of works wanted to find permuation matrix. AS you can see from photo given.

So I need to find permutation matrix for A(sc). But I couldn't figure out how to make on MATLAB. I use below codes, it gives irrevalent result. T

A=[-1 -1 1;1 -1 0;-3 0 1;1 0 0]
B = perms(A);

Answer 1

[Walter Roberson]

The description showed you the way:

ASc = [-1 -1 1;1 -1 0;-3 0 1;1 0 0]

ASc = 4×3

-1 -1 1 1 -1 0 -3 0 1 1 0 0

[LSc, USc, PSc] = lu(ASc)

LSc = 4×3

1.0000 0 0 -0.3333 1.0000 0 0.3333 1.0000 1.0000 -0.3333 0 1.0000

USc = 3×3

-3.0000 0 1.0000 0 -1.0000 0.3333 0 0 0.3333

PSc = 4×4

0 0 1 0 0 1 0 0 1 0 0 0 0 0 0 1

Note: the term "permutation matrix" in this context is not the same as is produced by perms() https://www.mathworks.com/help/matlab/ref/perms.html which "returns a matrix containing all permutations of the elements of vector v in reverse lexicographic order." The concepts do have a relationship, but perms() is not at all what you want for the purpose of building the kind of permutation matrix you need.