Matrix calculator
Type the matrix row by row: each row on a new line, numbers separated by spaces. Fractions like 1/3 are fine. Results are exact, with no rounding.
Result
- Rank
- 3
R1 : 2
R2 − (−3)·R1
R3 − (−2)·R1
R2 : 1/2
R1 − (1/2)·R2
R3 − (2)·R2
R3 : −1
R1 − (−1)·R3
R2 − (1)·R3
How to enter a matrix
Each row on a new line, numbers separated by spaces or commas. The 2 × 2 matrix with rows (1, 2) and (3, 4) is two lines: 1 2 and 3 4. You can paste a range of cells from a spreadsheet.
Gauss–Jordan elimination
The tool reduces the matrix to reduced row echelon form with row operations: swapping rows (R1 ↔ R2), dividing a row by a number and subtracting a multiple of another row. The list of operations appears below the result. The same procedure gives the determinant, rank, inverse and the solution of a linear system.
Common questions
When does a matrix have no inverse?
When its determinant is zero (a singular matrix). Then one row is a combination of the others.
Why are the results fractions?
Because they are exact. Tick “Show as decimals” if you prefer decimal numbers.