Row Reduction Calculator

The Row Reduction Calculator helps users perform matrix row reduction by allowing input of matrix dimensions, pivot method, and desired precision, and provides results including the row reduced matrix, its rank, determinant (for square matrices), potential solutions, and optional step-by-step reduction details.

Use Our Row Reduction Calculator

How to Use the Row Reduction Calculator

The Row Reduction Calculator is a convenient tool designed to assist in performing row reductions on matrices, finding matrix rank, determinants, and solutions to linear systems. Follow these steps to make the most out of the calculator.

Step 1: Enter Matrix Dimensions

  • Number of Rows: In the input field labeled “Number of Rows”, enter the number of rows your matrix contains. Ensure it is between 1 and 5.
  • Number of Columns: Enter the number of columns for your matrix in the field labeled “Number of Columns”. It should be between 1 and 6.

Step 2: Choose Pivot Selection Method

The calculator offers different methods for pivot selection during row reduction:

  • First Non-zero Entry: Select this option to use the first non-zero entry as the pivot.
  • Partial Pivoting: This method uses the largest absolute value in the column as the pivot.
  • Complete Pivoting: Choose this for searching the largest absolute value in the matrix for the pivot.

Select a method by choosing from the “Pivot Selection Method” dropdown menu.

Step 3: Set Decimal Precision

Enter the number of decimal places you want for your results in the “Decimal Precision” field. Choose a value between 1 and 10.

Step 4: Decide on Showing Intermediate Steps

Choose whether you want to see the intermediate steps of the row reduction process. Select “Yes” if you want the steps displayed, or “No” if you prefer only the final result.

Step 5: View the Results

After inputting your matrix and preferences, the calculator will provide the following results:

  • Row Reduced Matrix: The matrix after applying the row reduction, precision set by your input.
  • Matrix Rank: The rank of the reduced matrix, displayed with no decimals.
  • Determinant: If the matrix is square, the determined value will be displayed.
  • System Solution: Solutions to the system represented by the matrix (if applicable).
  • Reduction Steps: If ‘Show Intermediate Steps’ was set to “Yes”, detailed steps of the reduction process will appear.

Review your results and use them as needed for your further studies or problem-solving tasks.