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basis() and independent rows - Printable Version

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basis() and independent rows - salvomic - 06-13-2015 02:49 PM

I saw that basis() returns results with little differences in Home and CAS (in CAS I ge an apparently matrix, but if I put in the command like it is set(mat), in Home I get the matrix with the results)...

However, I need an idea to get from a matrix a list (other matrix, ok) with only the independent rows, using basis() or other commands...
Any idea?

An example:
I've the matrix M1 = [[2,1,4], [1,2,5], [5,1,7], [0,2,4]]
basis(M1) I get [[1,0,1], [0,1,2]]
(rank of M1 is 2, I see that i.e. 2*[1 0 1] + [0 1 2] is [2 1 4], the 1st row (also rd row is 5*[1 0 1]+ [0,1,2]), than it is dependent, no good, and so on..., but not "manually" got...
Only two rows are independent: 2, 4...

Thank you in advance!