Gauss Elimination Calculator

The Gauss Elimination Calculator allows users to solve systems of linear equations by inputting matrix coefficients and constants to find the values of variables with precision up to four decimal places.

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Using the Gauss Elimination Calculator

This guide will walk you through the steps required to operate the Gauss Elimination Calculator effectively. The calculator is designed to solve systems of linear equations using the Gauss Elimination method.

Step 1: Selecting Matrix Size

Begin by selecting the size of the matrix for your system of equations. The available options are 2×2, 3×3, and 4×4. Click on the dropdown menu labeled Matrix Size and choose the appropriate size for your calculation.

Step 2: Entering the Coefficients and Constants

Depending on the matrix size you selected, input fields for coefficients and constants will be available. Fill out these fields with the corresponding values from your system of equations:

  • For each equation, enter the values for the coefficients aij in the fields labeled a₁₁, a₁₂, a₁₃, etc.
  • Ensure all input fields are filled out as they are required for accurate calculation.
  • Also, provide the constant term bi for each equation in the fields labeled b₁, b₂, etc.

For example, if your first equation is 3x + 2y = 8 (for a 2×2 system), you would enter 3 into the field labeled a₁₁, 2 into a₁₂, and 8 into b₁.

Step 3: Performing the Calculation

Once all required fields are filled, the calculator will automatically apply the Gauss Elimination method to solve the system of equations. The solution will be displayed in the result fields.

  • The result fields labeled x₁, x₂, etc., will show the solutions to your system, rounded to four decimal places.

Step 4: Reviewing Results

Review the displayed results to ensure accuracy. These values represent the unknowns in your system of equations: x₁ for the first variable, x₂ for the second variable, and so forth.

If the results are not as expected, double-check the values entered in the input fields to ensure they match your system of equations accurately. Correct any errors and observe the updated results.

Additional Tips

Ensure that your system of equations has a unique solution. The Gauss Elimination method might not work correctly with dependent equations or if the matrix is singular. Double-check your equations to confirm that you have a valid system before entering them into the calculator.