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Hi I am trying to finish a proof about the fact that the row rank of any matrix is equal to the column rank.

I am stuck to try to show with a example, how the pivot columns span the columns of a matrix in the rref.

I have the matrix in the rref:

\begin{bmatrix} 1 & 0 \\ 0 & 1 \\ 0 & 0 \end{bmatrix}

And I do not know how to show that the pivot columns which in this case we have 2 span the column of the above matrix in the reduced row echelon form.

Can anyone help me on this?

Thanks

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