Characteristic Polynomial Calculator

How to Use the Characteristic Polynomial Calculator

This Characteristic Polynomial Calculator is designed to compute the characteristic polynomial of a 2×2 or 3×3 matrix. Follow these steps to use the calculator effectively:

Step 1: Select Matrix Size

Begin by specifying the size of the matrix you are working with. You can choose either a 2×2 matrix or a 3×3 matrix. This selection will determine the number of input fields that will be required:

• Select 2×2 Matrix if your matrix is 2 rows by 2 columns.
• Select 3×3 Matrix if your matrix is 3 rows by 3 columns.

Step 2: Enter Matrix Values

Once you’ve selected the matrix size, enter the values for each matrix element as prompted:

For a 2×2 Matrix:

• a₁₁: Enter the value of the first row, first column.
• a₁₂: Enter the value of the first row, second column.
• a₂₁: Enter the value of the second row, first column.
• a₂₂: Enter the value of the second row, second column.

For a 3×3 Matrix:

• a₁₁: Enter the value of the first row, first column.
• a₁₂: Enter the value of the first row, second column.
• a₁₃: Enter the value of the first row, third column.
• a₂₁: Enter the value of the second row, first column.
• a₂₂: Enter the value of the second row, second column.
• a₂₃: Enter the value of the second row, third column.
• a₃₁: Enter the value of the third row, first column.
• a₃₂: Enter the value of the third row, second column.
• a₃₃: Enter the value of the third row, third column.

Step 3: Obtain Results

Once all necessary matrix elements are entered, the calculator will compute the following results:

• Determinant: The determinant of your matrix, calculated with the appropriate formula for 2×2 or 3×3 matrices.
• Trace: The trace of your matrix, which is the sum of the main diagonal elements.
• Characteristic Polynomial: The polynomial expression of the characteristic polynomial.

The results are displayed with a precision of four decimal places, ensuring accuracy in calculations. You can view the characteristic polynomial in the format P(λ) = followed by the calculated equation.

By following these simple steps, you can efficiently compute the characteristic polynomial of any 2×2 or 3×3 matrix using the Characteristic Polynomial Calculator.