Performing calculations related to 3x3 square matrices. Part 5
Author: shiroeExecutions: 64
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Enter the elements of a 3x3 square matrix.
The numbers to the right of “Element” in the input fields correspond to the row and column indices of the matrix.
Please note that the output values may have the imaginary unit i appended to the right end.
Please be careful with negative signs when entering values.
The numbers to the right of “Element” in the input fields correspond to the row and column indices of the matrix.
Please note that the output values may have the imaginary unit i appended to the right end.
Please be careful with negative signs when entering values.
| Coefficient a0 | Coefficient of the λ³ term |
| Coefficient b0 | Coefficient of the λ² term |
| Coefficient c0 | Coefficient of the λ^1 term |
| Coefficient d0 | Coefficient of the λ^0 term |
| Coefficient a | Coefficient of the λ³ term (divided by the coefficient of the highest-order term) |
| Coefficient b | Coefficient of the λ² term (divided by the coefficient of the highest-order term) |
| Coefficient c | Coefficient of the λ^1 term (divided by the coefficient of the highest-order term) |
| Coefficient d | Coefficient of the λ^0 term (divided by the coefficient of the highest-order term) |
| x1 | Approximate Solution 1 (Numerical solution using the Durand-Kerner method) |
| x2 | Approximate Solution ② (Numerical Solution Using the Durand-Kerner Method) |
| x3 | Approximate Solution ③ (Numerical Solution Using the Durand-Kerner Method) |
| f(x1) | Verification (substituting into an expression divided by the coefficient of the highest-order term) |
| f(x2) | Verification (substituting into an expression divided by the coefficient of the highest-order term) |
| f(x3) | Verification (substituting into an expression divided by the coefficient of the highest-order term) |
| f0(x1) | Check Calculations |
| f0(x2) | Check Calculations |
| f0(x3) | Check Calculations |
| |x1| | Absolute Value of a Solution |
| |x2| | Absolute Value of a Solution |
| |x3| | Absolute Value of a Solution |
| |f(x1)| | The absolute value of the result obtained by substituting into an expression divided by the coefficient of the highest-order term |
| |f(x2)| | The absolute value of the result obtained by substituting into an expression divided by the coefficient of the highest-order term |
| |f(x3)| | The absolute value of the result obtained by substituting into an expression divided by the coefficient of the highest-order term |
| count | Number of loop iterations in the DK method. Displays -1 if not run. |
| R | The radius of a circle when an initial value is placed on the complex plane. If no value is entered, -1 is displayed. |
| xx[1] | Approximate Solution 1 (Factor Theorem) |
| xx[2] | Approximate Solution ② (Factor Theorem) |
| xx[3] | Approximate Solution ③ (Factor Theorem) |
Digit display setting: 50 digits. Fixed digits. Complex number calculation mode.
[Notes] (Superfluous):
Approximate values of real numbers are not necessarily real numbers. Complex numbers with similar absolute values (where the imaginary part is not zero) are also approximate values.
[Notes] (Superfluous):
Approximate values of real numbers are not necessarily real numbers. Complex numbers with similar absolute values (where the imaginary part is not zero) are also approximate values.
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We will list the coefficients of the characteristic equation of a 3x3 square matrix and calculate its solutions.
Let the form of the characteristic equation be a(λ³) + b(λ²) + cλ + d = 0.
(1) Find the coefficients of the characteristic equation of a 3x3 square matrix.
(2) Divide each coefficient by the coefficient (-1) of the highest-order term (3) in λ, and display the results.
(3) Display the approximate solution to the characteristic equation.
(4) As a verification check, display the results obtained by substituting the approximate solution into the equation.
(5) When the coefficients b, c, and d are integers, apply the Factor Theorem; if a solution is found, display the result.