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True or false If A and B have the same RREF then N(A) = N(B).

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True or false

If A and B have the same RREF then N(A) = N(B).

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Posted (Answer #1)

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True.

Let A be matrix of order  m x n .

So  also  has same order  m x n.

 Let rank of B = r= rank (A)

By rank nullity theorem

r(A)+N(A)=n

N(A)=n-r                        (i)

r(B)+N(B)=n

N(B)=n-r                        (ii)

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