Augmented Matrix Calculator

Using the Augmented Matrix Calculator

The Augmented Matrix Calculator is designed to help you solve systems of linear equations using advanced techniques. This step-by-step guide will walk you through the process of using the calculator effectively.

Setting Up the Calculation

Begin by entering the dimensions of the matrix:

• Number of Rows: Input the total number of rows in your augmented matrix. Ensure the value is between 1 and 10, inclusive, as per the calculator’s constraints.
• Number of Columns (Coefficient Matrix): Enter the number of columns present in the coefficient part of your augmented matrix. This should also be a value between 1 and 10.

Next, choose the method you wish to use for solving the system:

• Solution Method: Select between Gaussian Elimination and Gauss-Jordan Elimination from the dropdown options. Both methods are powerful tools for obtaining the solutions to a system of equations.

Interpreting the Results

Once you have input your matrix dimensions and chosen a solution method, the calculator provides you with a series of results:

• Reduced Matrix: Based on the chosen solution method, the calculator generates the reduced matrix form. This matrix is displayed with values rounded to four decimal places.
• System Solution: Using the reduced matrix, the calculator finds and displays the solution to the system, presented in the form “x = [solution]”.
• Determinant: The determinant of the coefficient matrix is calculated and shown, giving insight into the matrix’s properties. The determinant is rounded to four decimal places.
• Matrix Rank: The rank of the reduced matrix is determined and displayed as an integer value.
• System Classification: The system is classified based on the rank and determinant, indicating whether there is a unique solution, infinite solutions, or no solution at all. This is presented in a numerical format with an explanation of what each value represents.

Conclusion

By following these steps, you can use the Augmented Matrix Calculator to efficiently and accurately solve systems of linear equations. Make sure to enter valid data within the required constraints and interpret the calculator’s outputs for solving your systems effectively.