Determinant Calculator
Calculate a square matrix determinant with elimination steps.
Method
Gaussian elimination
Determinant
-2
Status
Determinant computed with Gaussian elimination.
Input matrix
The matrix used for the determinant calculation.
| Row | Column 1 | Column 2 |
|---|---|---|
| 1 | 1 | 2 |
| 2 | 3 | 4 |
Original matrix
Starting matrix.
| Row | Column 1 | Column 2 |
|---|---|---|
| 1 | 1 | 2 |
| 2 | 3 | 4 |
Swap row 1 with row 2
Move a stronger pivot into position.
| Row | Column 1 | Column 2 |
|---|---|---|
| 1 | 3 | 4 |
| 2 | 1 | 2 |
Eliminate below column 1
Clear the entries below the pivot.
| Row | Column 1 | Column 2 |
|---|---|---|
| 1 | 3 | 4 |
| 2 | 0 | 0.6667 |
Eliminate below column 2
Clear the entries below the pivot.
| Row | Column 1 | Column 2 |
|---|---|---|
| 1 | 3 | 4 |
| 2 | 0 | 0.6667 |
Formula
The determinant changes sign when rows are swapped. Gaussian elimination multiplies the pivots, while Bareiss elimination preserves exact values through fraction-free reduction.
Use the determinant calculator to enter a square matrix, pick Gaussian or Bareiss elimination, and inspect the row-reduction trail that leads to the determinant.
How to Use
Use the determinant calculator to enter a square matrix, pick Gaussian or Bareiss elimination, and inspect the row-reduction trail that leads to the determinant. Enter the Method and Matrix values and review the Method, Determinant, and Status outputs after you calculate.
- Open the calculator : Start with Determinant Calculator.
- Enter values : Fill in the required inputs and any optional settings.
- Review the result : Read the output and use the about page for more detail if needed.
Common Questions
What formula does the Determinant Calculator use?
The determinant changes sign when rows are swapped. Gaussian elimination multiplies the pivots, while Bareiss elimination preserves exact values through fraction-free reduction.