Gauss Jordan Calculator

Step-by-Step Guide to Using the Gauss Jordan Calculator

Step 1: Select the Matrix Size

Begin by selecting the size of the matrix you want to work with. The calculator allows you to choose from 2×2, 3×3, or 4×4 matrices. Use the dropdown menu labeled Matrix Size to make your selection. For this guide, we’ll focus on a 2×2 matrix as an example.

Step 2: Enter Matrix Values

After selecting the matrix size, you will need to input the values for each element of the matrix and the constants on the right-hand side of the equations. These fields are required and need to be entered for the calculator to perform the calculations. Set the following values for a 2×2 matrix:

• a₁₁: Enter the value for the first row, first column element.
• a₁₂: Enter the value for the first row, second column element.
• b₁: Enter the constant for the first equation.
• a₂₁: Enter the value for the second row, first column element.
• a₂₂: Enter the value for the second row, second column element.
• b₂: Enter the constant for the second equation.

Ensure that each value is entered as a number and pay attention to any validation messages, such as missing input or invalid format.

Step 3: Calculating the Results

Once all the necessary inputs are provided, the calculator will automatically compute the results. It uses the following logic:

• Determinant: Calculated using the formula (a₁₁ * a₂₂) – (a₁₂ * a₂₁). This determines the uniqueness of the solution.
• x₁: Calculated with ((a₂₂ * b₁) – (a₁₂ * b₂)) / Determinant.
• x₂: Calculated with ((a₁₁ * b₂) – (a₂₁ * b₁)) / Determinant.
• Solution Status: Displays No unique solution if the determinant is zero, indicating infinite or no solution. Otherwise, it shows Unique solution exists.

The results are displayed with the required precision, ensuring that numerical answers like x₁ and x₂ are shown to four decimal places.

Step 4: Interpreting the Results

Once the calculations are complete, review the results in the output section. The determinant provides insight into the possible solutions of the system. If the determinant is zero, the solution status will indicate that there is no unique solution. Otherwise, the values of x₁ and x₂ will provide the unique solution to your system of equations. Use these results to verify solutions or continue with further calculations as needed.