At the timestamp provided, there are instructions to transform a matrix by dividing the second row by the leftmost non-zero coefficient:
1 0.2
0 -0.95
resulting in the matrix
1 0.2
0 1
I’m not understanding how the -0.95 became 1 in the bottom right. If I’m understanding correctly, the entire second row [0 -0.95] would be divided by 1 (top left) as the leftmost non-zero coefficient, which just results in [0 -0.95] again. What am I missing?
Hi,
Each row is divided by the leftmost coefficient within that row. So, [0 -0.95] is divided by the leftmost non-zero coefficient which is -0.95.
So then, -0.95 divided by itself is how 1 is achieved?
That’s helpful, thanks! I didn’t expect that to be what is occurring.
I understand the term ‘leftmost non-zero’ can be misleading at first. But think about it. The ‘leftmost’ coefficient of the second row is 0, but ‘leftmost non-zero’ coefficient is -0.95.
If the matrix is 5x5 and the 3rd row is [0, 0, 1.5, 0, 3], then the ‘leftmost non-zero’ coefficient would be 1.5.
If the matrix is 5x5 and the 3rd row is [0, 0, 0, 0, 0], then the ‘leftmost non-zero’ coefficient does not exist. So you don’t need to do anything on the 3rd row.
