why mod(rref(A), 2) does not give the correct result?

Lets say I have the followings all in mod 2

a = [1 1 0 0 0]'

a = 5×1

1 1 0 0 0

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b = [1 0 1 0 1]'

b = 5×1

1 0 1 0 1

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c = [0 1 1 0 1]'

c = 5×1

0 1 1 0 1

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clearly, c = a + b in mod 2

However when I run the command

mod(rref([a b c]), 2)

ans = 5×3

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

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It does not give the corret result for linear combination in mod 2? My expect answer should be:

expected_ans = [1 0 1; 0 1 1; 0 0 0; 0 0 0; 0 0 0]

expected_ans = 5×3

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

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Could anyone explain why?

Answer 1

[David Goodmanson]

Hi Lily,

Although c is a linear combination of a and b mod 2, rref does not know anything about mod 2.

rank([a b c])

 ans =  3

As far as rref is concerned, a, b and c are linearly independent ('mod' not being a linear operation under the usual addition of numbers). So you get three nonzero rows.