Read the result
Only the target row changes for a replacement or scaling operation. A swap changes row order but not the equations represented by the system.
Matrix methods
Matrix Row Operations Visualiser
Try a single row operation and see exactly which entries change.
Formula
R_i <-> R_j, R_i <- kR_i, or R_i <- R_i + kR_j
Result
Worked substitution
Row operations are the mechanics behind Gaussian elimination. The notation matters because it tells you which row changes.
Where it helps
Use this to rehearse the row notation used inside Gaussian and Gauss-Jordan elimination.
Common slip
Scaling a row by 0 destroys information, so it is not an equivalent row operation.
Try it
Use R2 <- R2 + 1.5R1 on the default matrix and compare the new row with the Gaussian elimination step.