Technical Calculator

Characteristic Polynomial Calculator

Size of the Matrix:

Matrix

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The feature polynomial calculator computes the function polynomial of a rectangular matrix 2×2, 3×three, four×4, or any order matrix.

Characteristic Polynomial:

The function polynomial of a square matrix is a polynomial containing eigenvalues as roots. The feature polynomial equation is derived by way of equating the polynomial to 0.

“ f(λ) and the formula is given through the f(λ) = det (A – λIn) “

det (A - λI) = 0

In which:

A is a matrix λI is the identification matrix increased via “λ”

We want to discover the eigenvalues, λ, and A.

Det is the determinant of the matrix If the function polynomial is equated to 0, then our ensuing equation is referred to as the function polynomial equation, it is also called the determinant equation.

If all the roots of the feature equation are, we can say the manage machine is strong and if all the roots are bad then the manipulate device is considered to be greater volatile. The moderation gadget has fantastic and bad values, whilst determined with the aid of the function equation calculator.

The way to discover function Polynomial of a 3&instances; 3 Matrix?

Discover the characteristic polynomial of the matrix having 3 rows and three columns.

$$ \begin{bmatrix}4 & 6 & 3 \\ 2 & 8 & 5 \\ 1 & 7 & 6 \\\end{bmatrix} $$     

Solution:

$$ \begin{bmatrix}4 & 6 & 3 \\ 2 & 8 & 5 \\ 1 & 7 & 6 \\\end{bmatrix} $$  

Subtract the “λ” from the diagonal elements of the original matrix to find:

$$ \begin{bmatrix}4-\lambda & 6 & 3 \\ 2 & 8-\lambda & 5 \\ 1 & 7 & 6-\lambda \\\end{bmatrix} $$ 

The function polynomial is the determinant of the received matrix. resolve the determinant of this 3&instances;three matrix:

$$ = -\lambda^{3} + 18\lambda^{2} - 59\lambda + 44 $$

you can use the characteristic polynomial calculator to clear up the linear differential function polynomial or function roots. It reduces the steps of solving an extended equation, as you may find the roots in a count number of moments via the use of the function polynomial equation.                             

How Does a feature Polynomial Calculator with Steps paintings?

The characteristic polynomial of the matrix calculator calls for the subsequent fee to find the function polynomial equation.

Input:

  • Enter the dimensions of the matrix
  • Enter all of the coefficient values
  • Hit the calculate button

Output:

  • The feature polynomial equation ;