Well, to get the matrix into row echelon form, we want to get zeros in the bottom-left triangle. The only way to do that with elementary row operations is to combine each row with some proportion of another row. When tackling the first-column entry of row 2, I found that row 3 wouldn't work, since its first-column value was zero. The only remaining option was row 1. is our first choice, but we can kill two birds with one stone by dividing all that by 3:Originally Posted by keisanhen
...or...
This not only makes the first-column entry a zero, but it makes the second-column entry a 1, which is also necessary for row echelon form.