[Math] Finding the rank of a matrix using gauss jordan method

Question

Find the rank of the matrix \begin{bmatrix} 1 & -1 & 2 & 1 \\ 1 & 2 & 1 & -2 \\ 1 & 1 & 1 & -1 \end{bmatrix}

After reducing it to row echelon form I got as follows
$$\begin{bmatrix} 1 & -1 & 2 & 1 \\ 0 & 1 & 0 & -1 \\ 0 & 0 & 1 & 0 \end{bmatrix}$$

My Conclusion

Since there are $3$ non-zero rows, the rank of the matrix is $3$

Is my conclusion correct?

Answer 1

You have $3$ pivot columns so the rank is $3$. Yes you are right in this case, but the rank number is equal to the number of pivot columns after you make echelon form, not the number of non-zero rows.