This is from a video in an online course. The lesson is on finding the inverse of a matrix using reduced row echelon form. The row operations the instructor uses here are not making sense to me.
R1: [1 2 3] R2: [0 1 3]
Shouldn't R1 - 2(R2) for column 3 be 3 - 2(3) = 3 - 6 = -3, not -4?
Yes, you are indeed correct; the screenshot from the video has the mistake you identify, and hence, is incorrect. (The same problem on occasion happens in textbooks, and sometimes professors make silly mistakes, or typos, too).
Just one additional comment, some prefer the notation that indicates row operations and the target row. E.g., in this case, some (and I) would right $[R_1-2R_2] \to R_1$, to make explicit that we are reassigning new values to $R_1$, by using the original values of $R_1$ and subtracting $2R_2$ from those values.