1. Let's start by understanding what pivot rows and pivot columns are in the context of a matrix. 2. A pivot position in a matrix is the first nonzero entry in a row after the matrix has been transformed into row echelon form (REF) or reduced row echelon form (RREF). 3. The pivot row is the row that contains a pivot position. 4. The pivot column is the column that contains a pivot position. 5. To find pivot rows and columns, you typically perform Gaussian elimination to get the matrix into REF or RREF. 6. For example, consider the matrix $$\begin{bmatrix}1 & 2 & 0 \\ 0 & 3 & 4 \\ 0 & 0 & 5\end{bmatrix}$$. 7. The pivots are the first nonzero entries in each row: in row 1, pivot is 1 in column 1; in row 2, pivot is 3 in column 2; in row 3, pivot is 5 in column 3. 8. Therefore, the pivot rows are rows 1, 2, and 3. 9. The pivot columns are columns 1, 2, and 3. 10. In summary, pivot rows and columns correspond to the positions of leading entries in the matrix after row reduction. This explanation applies to any matrix you analyze for pivots.