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`CP = -λ^3+"tr"(A)λ^2+1/2("tr"(A)^2-"tr"(A^2))λ+det(A)`

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The **characteristic polynomial of a 3x3 matrix** calculator computes the characteristic polynomial of a 3x3 matrix.

**INSTRUCTIONS:** Enter the following:

- (
**A**) 3x3 matrix

**Polynomial (CP):** The calculator returns the:

- Characteristic Polynomial of
**A** - Trace of
**A** - Determinant of
**A**

- Determinant of 3-by-3 Matrix
- Characteristic Polynomial of a 3x3 matrix
- Product of a 3x3 matrix and a 3x1 matrix
- Inverse of a 3x3 Matrix
- Transpose of a 3x3 Matrix
- Trace of a 3x3 Matrix
- Mirror of a 3x3 Matrix
- Cramer's Rule (three equations, solved for x)
- Cramer's Rule (three equations, solved for y)
- Cramer's Rule (three equations, solved for z)
- Cramer's Rule Calculator

The **characteristic polynomial (CP)** of an nxn matrix `A` is a polynomial whose roots are the eigenvalues of the matrix `A`. It is defined as `det(A-λI)`, where `I` is the identity matrix. The coefficients of the polynomial are determined by the determinant and trace of the matrix.

For the 3x3 matrix A:

A = `[[A_11,A_12, A_13],[A_21,A_22,A_23],[A_31,A_32,A_33]]`,

the characteristic polynomial can be found using the formula `-λ^3+"tr"(A)λ^2+1/2("tr"(A)^2-"tr"(A^2))λ+det(A)`, where `"tr"(A)` is the trace of 3x3 matrix A and `det(A)` is the determinant of 3x3 matrix A.

For the Characteristic Polynomial of a 2x2 matrix, CLICK HERE