Performing calculations related to 3x3 square matrices. Part 4.
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The coefficients of the characteristic equation are initially displayed without dividing each coefficient by the coefficient of the highest-degree term (the x³ term).
(Displayed as [Before Processing].)
Next, the coefficients are displayed after division.
Outputs the minor determinants. The numbers on the right are indices representing rows and columns (row, column = 1, 2, 3).
These correspond to the rows and columns of the input matrix.
Outputs the cofactors. The numbers on the right are indices representing rows and columns (row, column = 1, 2, 3).
These correspond to the rows and columns of the input matrix.
Outputs the cofactor matrix. The numbers on the right are indices representing the
rows and columns of the calculated cofactor matrix (rows, columns = 1, 2, 3).
Calculates the determinant of the input matrix.
If the result of the determinant calculation is not 0, the inverse is also calculated and output.
(Displayed as [Before Processing].)
Next, the coefficients are displayed after division.
Outputs the minor determinants. The numbers on the right are indices representing rows and columns (row, column = 1, 2, 3).
These correspond to the rows and columns of the input matrix.
Outputs the cofactors. The numbers on the right are indices representing rows and columns (row, column = 1, 2, 3).
These correspond to the rows and columns of the input matrix.
Outputs the cofactor matrix. The numbers on the right are indices representing the
rows and columns of the calculated cofactor matrix (rows, columns = 1, 2, 3).
Calculates the determinant of the input matrix.
If the result of the determinant calculation is not 0, the inverse is also calculated and output.
| k0 [Before Processing] | (Coefficient of the λ³ term) |
| k1 [Before Processing] | (Coefficient of the λ² term) |
| k2[Before processing] | (Coefficient of the λ^1 term) |
| k3 [Before Processing] | (Constant term) |
| k0 | |
| k1 | |
| k2 | |
| k3 | |
| Minor Δ11 | Minor Δ12 Minor Δ13 |
| Minor Δ21 | Minor Δ22 Minor Δ23 |
| Minor Δ31 | Minor Δ32 Minor Δ33 |
| Cofactor 11 | Cofactor 12 Cofactor 13 |
| Cofactor 21 | Cofactor 22 Cofactor 23 |
| Cofactor 31 | Cofactor 32 Cofactor 33 |
| Residue Matrix 11 | Residue Matrix 12 Residue Matrix 13 |
| Residue Matrix 21 | Residue Matrix 22 Residue Matrix 23 |
| Residue Matrix 31 | Residue Matrix 32 Residue Matrix 33 |
| Value of the determinant | |
| Reciprocal of a determinant |
R6 (2024).02/23 (Fri)_ver.003
Updated to R6 (2024).03/24 (Sun)_ver.004.
R6 (2024).03/24 (Sun)_Added.
Updated to R6 (2024).03/24 (Sun)_ver.004.
R6 (2024).03/24 (Sun)_Added.
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1) Output the coefficients of the characteristic equation. Assume the characteristic equation is of the form k0λ^3 + k1λ^2 + k3λ + k4 = 0.
2) Calculate the value of the minor.
3) Calculate the value of the cofactor.
4) Compute the cofactor matrix.
5) Compute the value of the determinant using Saras’s diagram.
6) If the value of the determinant computed using Saras’s diagram is not zero, compute the inverse.