Rref Calculator

Rows separated by a semicolon or newline, entries by spaces or commas.
Reduced matrix
1 0 0 2; 0 1 0 3; 0 0 1 -1
RREF and Gauss-Jordan Calculator
Rank
3
Nullity
1
Rows
3
Columns
4
Pivot columns
1, 2, 3
Free columns
4
System is consistent
n/a
Null space basis
(-2, -3, 1, 1)
Form produced
Reduced row echelon form
Worked out from Gilbert Strang, Introduction to Linear Algebra, ch. 3 (the four subspaces, rank, RREF) and 1 other source.

How this is worked out

9 steps
  1. Starting 3x4 matrix:
  2. [ 2 1 -1 8 ]
  3. [ -3 -1 2 -11 ]
  4. [ -2 1 2 -3 ]
  5. Gauss-Jordan elimination: scale each pivot row to a leading 1 and clear the entries above and below it.
  6. [ 1 0 0 2 ]
  7. [ 0 1 0 3 ]
  8. [ 0 0 1 -1 ]
  9. Rank 3, nullity 1 (rank + nullity = 4 columns).
Reduced matrixtable
0123
1002
0103
001-1

Results are general information, not financial, tax, legal, medical or engineering advice.