Null space of a matrix and row echelon form

Question

can we say N(A) = N(rref(A)) = N(Row echelon form A)? I was watching a video about that and instructor(khan acamdey) stated that N(A) = N(rref(A)) but not stated Row echelon form, it may be uunneccessary to emphasize that but should it be true right ?

score 1 · Accepted Answer · answered Oct 29 '21 at 12:50

1

Yes, the null spaces of $A$, row echelon form of $A$ and reduced row echelon form of $A$ are equal. This is because elementary row operations preserve the null space of a matrix.

answered Oct 29 '21 at 12:50

Minus One-Twelfth

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Null space of a matrix and row echelon form

1 Answers1