Math basics › Linear algebra
Row reduction
Three legal moves
Swap two rows, multiply a row by a nonzero number, or add a multiple of one row to another. Nothing else.
The goal
Echelon form: each row's first nonzero entry (its pivot) sits to the right of the one above, with zeros below it.
Reading the answer
A row 0 0 0 | 5 means no solution. A column with no pivot is a free variable, which means infinitely many solutions.
Keep the whole row
Every move applies to the entire row, including the numbers after the bar. Most mistakes are one forgotten entry.