

then repeat this process in the next column, and so on. Identify the matrices in your reduction process for B that appear at the pivot identification stages (right before you begin clearing beneath each of the pivots). In each such matrix, circle the newly identified pivot and the entries below that pivot. Column by column, compare your circled entries with the corresponding entries in the unit lower triangular matrix L from your decomposition in Step 2. What do you notice? [Hint: You may want to look at the reduction of A and its corresponding decomposition from Part 1 to verify your observation.]

