REF/RREF Study Tool
Instructions
Type the entries of a matrix below to check whether it is in row echelon form (REF), reduced row echelon form (RREF), or neither. Every condition that fails is listed along with the entries that break it; point at a reason to highlight those entries in the matrix. For a matrix in REF, the page also gives the rank and nullity and the number of solutions of the system, with the reason.
To practice, switch to Quiz: the page shows a random matrix, and you decide which conditions it satisfies and which form it's in, then check your answers.
Entries can be integers, decimals, or fractions such as -2, 0.5, or
1/3. Blank entries count as 0. Use the arrow keys or Enter to move between entries
(Shift+Enter moves up).
Leading entry Breaks a condition (colored by condition; see the list below)
Is this matrix in REF, RREF, or neither?
Instructions
Answer yes or no for whether each condition is true of the matrix, then choose its form. Answer as many as you like: it's fine to skip the conditions and just choose the form. Click a selected answer again to unselect it. When you check your answers, the leading entries are circled and each condition is explained below.
Optional: first click the leading entries in the matrix to circle them, and click the row labels (R1, R2, …) to mark the zero rows. These marks are checked too.
Part 2: Rank, nullity, and solutions
Since the matrix is in REF, you can find these from its leading entries. When you check your answers, the explanation appears below.